Finally, I looked at some odds calcs to see where I was (I had a general idea when I was making my decision, but I always like to look afterward in a hand like this)
Up against 2 pair -- ~50/50
Up against 55, 66, or 77 -- ~70/30 dog
Up against 10's or better -- ~60/40 dog
Up against 99 -- ~75/25 dog
Up against 89 -- ~85/15 dog and that's to chop (< 2% chance of winning outright)
Up against 34 -- ~70/30 dog
I listed those above in the order that I thought he might be holding. I'm not including lesser holdings that he could have that I'm smashing (33, 44, 78, 45, A7, 9-10).
Based on how the hand played, I thought there was no chance he's holding AA or KK. I also wasn't expecting 34 at all (honestly didn't even consider that in my decision making). And I thought 89 was pretty unlikely with my 88.
I had him on 2 pair or possible set. Up against 2 pair, I thought the odds had me slightly behind. Up against a set, I thought it was more like 60/40, but either way, both would be ok.
I think he's folding anything except 34, 89, a set, and likely AA and KK to a reraise all-in. Two pair he MIGHT call. Even 10's or J's he likely lays it down to a reraise to his call. And since I figured the only thing he might have out of that that he's not folding is a set or 2 pair, I thought the raise was a good play. I'm either getting him to lay down a better hand (9's or higher or 2 pair) or I want the call from him.