The Ministry had to sort out which people who worked with Death Eaters were Imperiused.
Arthur Weasley, as an employee of the Ministry of Magic, would have been working there when the Ministry was helping determine after the first war which people engaged in Death Eater activities were under the Imperius Curse and which were doing it willingly.
“Years back, there were a lot of witches and wizards being controlled by the Imperius Curse,’ said Moody, and Harry knew he was talking about the days in which Voldemort had been all-powerful. ‘Some job for the Ministry, trying to sort out who was being forced to act, and who was acting of their own free will.”
- Harry Potter and the Goblet of Fire, Chapter 14 (The Unforgivable Curses)
Many Death Eaters claimed to be Imperiused to avoid sentencing, and the Ministry had to figure out which people really were.
“Avery – from what I’ve heard he wormed his way out of trouble by saying he’d been acting under the Imperius Curse – he’s still at large.”
- Harry Potter and the Goblet of Fire, Chapter 27 (Padfoot
Returns)
Everyone working at the Ministry would have likely been familiar with the Imperius Curse, because either they or their colleagues would have been involved in figuring out who was under it. Arthur might not have been actively participating in figuring out who were Death Eaters and who weren't, but he was still working at the Ministry where the effects of the Imperius Curse would have been common knowledge.
The Death Eaters did indeed use the Imperius Curse as part of their tactics, for example on Broderick Bode.
“Bode could never have taken it, Master … Bode would have known he could not … undoubtedly, that is why he fought so hard against Malfoy’s Imperius Curse …”
- Harry Potter and the Order of the Phoenix, Chapter 26 (Seen and Unforeseen)
In addition, the Death Eaters also used it on Ministry officials like Pius Thicknesse, in order to gain power and control over the Ministry. So it seems plausible that, during the first war, all Ministry officials would be instructed to watch for signs of their colleagues being Imperiused.
“My Lord, I have good news on that score. I have – with difficulty, and after great effort – succeeded in placing an Imperius Curse upon Pius Thicknesse.”
- Harry Potter and the Deathly Hallows, Chapter 1 (The Dark Lord Ascending)
They planned to get more Ministry officials under their control as well, so it seems likely that during the first war, the Ministry might have instructed its staff to watch for their colleagues possibly being Imperiused. If this was the case, then all departments would likely be given the same warnings, which would reach Arthur Weasley as well since he was a Ministry employee.
“It is a start,’ said Voldemort. ‘But Thicknesse is only one man. Scrimgeour must be surrounded by our people before I act. One failed attempt on the Minister’s life will set me back a long way.”
- Harry Potter and the Deathly Hallows, Chapter 1 (The Dark Lord Ascending)
During the second war, for example, they had placed people within the Department of Magical Transport, possibly by having Imperiused them.
“We now have several people planted within the Department of Magical Transport. If Potter Apparates or uses the Floo Network, we shall know immediately.”
- Harry Potter and the Deathly Hallows, Chapter 1 (The Dark Lord Ascending)
By using the Imperius Curse the Death Eaters are able to stage a successful and stealthy coup of the Ministry.
“The coup has been smooth and virtually silent,’ said Lupin. ‘The official version of Scrimgeour’s murder is that he resigned; he has been replaced by Pius Thicknesse, who is under the Imperius Curse.”
- Harry Potter and the Deathly Hallows, Chapter 11 (The Bribe)