Harry was his enemy - and Avada Kedavra failed on Harry before.
Even when Harry was a baby (which are fairly easy to kill), and the Dark Lord had no reason to think he wouldn’t be able to kill him, he was being very cautious about wanting to make sure the boy who was foretold as the one who could destroy him was killed. He wanted to watch, to make sure Harry died, even when there was no reason to believe he wouldn’t.
“He pointed the wand very carefully into the boy’s face: he wanted to see it happen, the destruction of this one, inexplicable danger.”
- Harry Potter and the Deathly Hallows, Chapter 17 (Bathilda’s Secret)
The curse of course failed, and between the night he first tried to kill Harry and then when Harry seemed to be dead, the Killing Curse failed to work on Harry three times; as a baby, in the graveyard because of the twin cores, and when Harry’s wand acted against the wand borrowed from Lucius. He was cautious to see Harry’s destruction when it seemed guaranteed - after having Avada Kedavra fail on Harry three times, it’s logical he’d want to check.
Up until that point, nothing he’d tried worked - Harry survived the Killing Curse three times, as well as burned Quirrell with his touch enough to kill him, destroyed the diary, resisted possession in the Ministry, and avoided the Dark Lord’s capture despite being highly searched for. Harry had thwarted him several times by that point, so it was logical he’d want to make sure that Harry was really dead.
If you believe you’ve killed the only person who can destroy you, especially if they have a habit of surviving when they shouldn’t, it makes sense to check if they’re indeed actually dead.