The short story "Hindsight" by Jack Williamson matches your description perfectly. (The story was first published in Astounding Science-Fiction, May 1940, available at the Internet Archive. You may have read it in a Georgian translation of the Asimov-Greenberg-edited anthology The Great Science Fiction Stories Volume 2, 1940—do any of the other contents seem familiar?) Taking it point by point:
A man has created a Super Weapon for an empire.
The empire is the Astrarchy, founded by space pirates, based in the asteroid belt, and bent on conquering the whole solar system:
His voice was injured and defiant. "But, so far as I'm concerned, the Astrarchy is just as respectable as such planet nations as Earth and Mars and the Jovian Federation. And it's a good deal more wealthy and powerful than any of them."
Tense-faced, the Martian girl shook her dark head. "Don't blind yourself, Bill," she begged urgently. "Can't you see that the Astrarch really is no different from any of the old pirates? His fleets still seize any independent vessel, or make the owners ransom it with his space-patrol tax."
She caught an indignant breath. "Everywhere—even here on Mars—the agents and residents and traders of the Astrarchy have brought graft and corruption and oppression. The Astrarch is using his wealth and his space power to undermine the government of every independent planet. He's planning to conquer the system!"
The super weapon is an autosight for spaceship guns:
Beneath those thrusting eyes, Brek Veronar flinched. "Thank you, Gorro," he gulped—he was among the few privileged to call the Astrarch by name. "Later, perhaps. But the torpedo guide isn't finished. And I've several ideas for improving the autosight. I'd much prefer to stay in the laboratory."
For an instant, the short man's smile seemed genuine. "The Astrarchy is indebted to you for the autosight. The increased accuracy of fire had in effect quadrupled our fleets." His eyes were sharp again, doubtful. "Are further improvements possible?"
Brek Veronar caught his breath. His knees felt a little weak. He knew he was talking for his life. He swallowed, and his words came at first unsteadily.
"Geodesic analysis and integration is a completely new science," he said desperately. "It would be foolish to limit the possibilities. With a sufficiently delicate pick-up, the achronic detector fields ought to be able to trace the world lines of any object almost indefinitely. Into the future—
He paused for emphasis. "Or into the past!"
But, one day, another battle, before he presses the button, something happens.
When he wakes up, the ship is damaged, the empire lost, everyone in shock.
"The Queen is disabled. Reaction batteries shot away, and main power plant dead. Repair is hopeless. And our present orbit will carry us far too close to the sun. None of our ships able to undertake rescue. We'll be baked alive."
"How were we beaten?" demanded Brek. "I can't understand!"
:"Marksmanship," said the tired Astrarch. "Tony Grimm has something better than your autosight. He shot us to pieces before we could find the range." His face was a pale mask of bitterness. "If my agents had employed him, twenty years ago, instead of you—" He bit blood from his lip. "But the past cannot be changed."
Brek was staring at the huge, silent bulk of the autosight. "Perhaps"—he whispered—"it can be!"
He remembers and decides that one event in his past had affected this battle. Years ago, that girl wrote a letter to him and invited him to a party (or rendezvous). So his friend had more time for learning and developed a similar but more powerful weapon, which helped the rebels to win the battle. He suggests to use the energy left to make a change in the past and make that girl write a letter to his friend, not to him, giving him a advantage in time.
"What's this?" rasped the anxious Astrarch. "A schoolgirl writing a note—what has she to do with a space battle?"
Brek scanned the fiery symbols. "She was deciding the battle—that day twenty years ago!" His voice rang with elation. "You see, she had a date to go dancing in Toran with Tony Grimm that night. But her father was giving a special lecture on the new theories of achronic force. Tony broke the date, to attend the lecture."
As Brek watched the motionless image in the cube his voice turned a little husky. "Elora was angry—that was before she knew Tony very well. I had asked her for a date. And, at the moment you see, she has just written a note, to say that she would go dancing with me."
Brek gulped. "But she is undecided, you see. Because she loves Tony. A very little would make her tear up the note to me, and write another to Tony, to say that she would go to the lecture with him."
The Astrarch stared cadaverously. "But how could that decide the battle?"
"In the past that we have lived," Brek told him, "Elora sent the note to me. I went dancing with her, and missed the lecture. Tony attended it—and got the germ idea that finally caused his autosight to work better than mine.
"But, if she had written to Tony instead, he would have offered, out of contrition, to cut the lecture—so the analyzers indicate. I should have attended the lecture in Tony's place, and my autosight would have been better in the end."
The Astrarch's waxen head nodded slowly. "But—can you really change the past?"
Brek paused for a moment, solemnly. "We have all the power of the ship's converters," he said at last. "We have the high-frequency achronic field, as a lever through which to apply it. Surely, with the millions of kilowatts to spend, we can stimulate a few cells in a schoolgirl's brain. We shall see."
But in the last second before proceeding he looks at a watch his old friend and that girl (love from past) gifted him a long time ago. His feelings don't allow him to do it. So he left his past untouched.
Two minutes! Brek looked down at the jeweled chronometer on his wrist. For a moment he had an odd feeling that the design was unfamiliar. Strange, when he had worn it for twenty years.
The dial blurred a little. He remembered the day that Tony and Elora gave it to him—the day he left the university to come to Astrophon. It was too nice a gift. Neither of them had much money.
He wondered if Tony had ever guessed his love for Elora. Probably it was better that she had always declined his attentions. No shadow of jealousy had ever come over their friendship.
"Minus one—"
This wouldn't do! Half angrily, Brek jerked his eyes back to the screen. Still, however, in the silvery sodium clouds, he saw the faces of Tony and Elora. Still he couldn't forget the oddly unfamiliar pressure of the chronometer on his wrist—it was like the soft touch of Elora's fingers, when she had fastened it there.
Suddenly the black flecks in the screen were not targets any more. Brek caught a long gasping breath. After all, he was an Earthman. After twenty years in the Astrarch's generous pay, this timepiece was still his most precious possession.
His gray eyes narrowed grimly. Without the autosight, the Astrarch's fleet would be utterly blind in the sodium clouds. Given any sort of achronic range finder, Tony Grimm could wipe it out.
Brek's gaunt body trembled. Death, he knew, would be the sure penalty. In the battle or afterward—it didn't matter. He knew that he would accept it without regret.
In the end he says to the empire admirals that they can't do anything more, because their loss has permanently reflected in time and can't be changed.
"Once you told me, Veronar, that the past could be changed. Then I wouldn't listen. But now—try anything you can. You might be able to save yourself from the unpleasantness that my men are planning."
Looking at the muttering men, Brek shook his head. "I was mistaken," he said deliberately. "I failed to take account of the two-way nature of time. But the future, I see now, is as real as the past. Aside from the direction of entropy flow and the flow of consciousness, future and past cannot be distinguished."
"The future determines the past, as much as the past does the future. It is possible to trace out the determiner factors, and even, with sufficient power, to cause a local deflection of the geodesics. But world lines are fixed in the future, as rigidly as in the past. However the factors are rearranged, the end result will always be the same."
