This is "Digging for the Bones" by Pannageid.
Ginny attempts suicide with a potion
(Chapter 23)
"Sir." gasped Harry, "Ginny Weasley. She's taken a potion. It's bad. In the common room."
"It looks like an overdose of a Draught of Peace. There's residue still in her mouth." said Snape, quickly, "Her heart stopped.
Snape, McGonagall, and Pomfrey save her with a spell
(Chapter 23)
"Lloyd, Granger, step away." said Snape, taking McGonagall's hand. Madam Pomfrey took the other. Pomfrey and Snape aimed their wands at Ginny who jerked where she lay on the floor. Snape said a long, harsh sounding incantation and there was a flash of white light.
The spell drains their life force
(Chapter 23)
"We were able to restart her heart, because her brain was still alive. To put it simply, we had to part with some of our own life energy.
Snape uses a cane
(Chapter 24)
He summoned a quill from a nearby table and transfigured it into a cane for balance. If he was going to need a walking stick for any length of time, he was going to have to get himself a properly ominous looking one.
Harry helps Snape
(Chapter 24)
"What, Potter?" Severus growled, leaning his head back.
"Can I get you something?" Potter asked, softly.
And continues to help him in other ways in the ensuing story.
The Weasley's owe him a debt
(Chapter 34)
Tribuo Vita creates a bond deeper than a life debt. In some circles, it is accepted as being as binding as blood. Again, we see the similarity to certain Dark Rituals, although Healing Oaths...
Wonderful. Severus was now an honorary Weasley. Minerva already was a distant Weasley cousin and Poppy had taken all of the Healer Oaths which negated life debts. Chances were, they nullified this as well.
Harry gets along with Snape's neighbor (though it's not at the beginning of the story)
(Chapter 31)
Mrs. Cook's house was built on the same basic plan as Professor Snape's, but it was in immaculate order. She led him into the kitchen which was more modern and up to date that1 the one next door. She indicated the table to Harry, "Just put the things there, then." she said."
Snape (and Harry) stays at the Weasleys
(Chapter 48)
Severus replied, "Professor Lupin has some pressing business tonight and tomorrow at Hogwarts. Madam Pomfrey feels that we need some help while he's gone. MR. and Mrs. Weasley have invited us to stay with them."
(Chapter 50)
Severus took the cane that Mrs. Weasley bent down to pick up from the ground and offered to him. He pulled his arms from the grasp of the two Weasley men. "And then, if you could just show me where you'd like me to sleep, Mrs. Weasley."
They are worried that Snape will ask for Ginny's hand
(Chapter 50)
Molly apparently read the confusion on his face, "Professor... Severus," she said softly, "the soul bond gives you the right to ask for Ginny's hand. In marriage."
But Snape refuses
(Chapter 50)
"Please put your minds at rest – I have no intention of exercising this particular prerogative."
The story is long
It has 62 chapters.
Found by searching for "snape saves ginny" which returned this Reddit thread which mentioned the story's name. I simply looked through the story until I found the corroborating details.
1. This should probably say "than".
