I have ~$240; Villain covers.

Villain is a white male in his early 50s. I've never played with him before. In the limited time I've had to observe him, I've noticed that he is not very sophisticated with bet-sizing and that he will limp with big pairs. He has not made a preflop raise yet.

To clarify the bet sizing point, there was a bet of 50 and a call and he raised to 100 with QQ on a J-T-9-8 turn (with a flush draw) when there were 3-4 players in the hand and a real raise was definitely in order.

Two limpers, including Villain, I raise to 14 in the HJ with 99, a very tight old man calls on the button, and Villain calls.
Flop (45): T-9-8
Villain checks, I bet 45, Button folds, Villain raises to 90 fairly quickly, I snap call.
Turn (225): A
Villain asks to see my chips and then shoves. I (~135 behind) ???

Thoughts about any of this?

You are pretty much always beat here, unless villain is spewy. Its several combos of both flushes and straights out there, as well as two bigger sets than yours. I cant see villain minraising you on the flop and shipping allin on the turn with a hand you beat.

This should be a trivial fold, even though it sucks to flop middle set on this kind of board.

Meh fold.
I think the more interesting question is what should our flop sizing be if we bet at all?

I prefer $35 or so here as I think it gets looked up weaker.

+1

I actually dont think checking this flop and see a turn is bad at all.

Checking behind for pure pot control reasons I think is great. Imagine you do same bet and tight villian folds and other villian and extremely loose and ships? Such a bad spot for you but you probably have to call

If he's always doing this with flushes (and possibly straights) this is a fold. However calling isn't terrible. You have 23% equity on turn agains a flush or straight and you need 27% equity to break even. If he can ever do this with Worse hands like AT or Acxx then it's a call.

Bet flop always. And shove turn if flatted on flop

I cant fold. GII on flop IMO before any scare cards come. The board is way too wet to fold.

He could have sd/fd combos/2 pair and lower set which we are crushing. We are behind made straights and flushes but still have equity.

do the math, we know what he has so we just need the numbers to add up.

I like your flop bet though, super wet OMC can have a ton of hands here that will call flop.