Middle of the tournament, I'm in the BB and Villain is UTG+1. He doesn't seem particularly great but not a total idiot either.

Can't remember stack sizes exactly, these are my best approximations
UTG: 12bb, limps
UTG+1 (Villain): 22bb, limps
folds to BTN: 30bb, limps
SB completes
Hero: 30bb, Ks7c, checks

Don't think it makes a whole lot of sense to iso raise, hand doesn't play very well post flop, out of position, players have been limp calling a lot.

Flop (5bb): 7s5c3c
SB checks, I lead out for 3.5bb. Lots of hands that I can get value from (87-Q7 are all capable of limping, A5-A2 and any overcard or club/straight draws. I could absolutely be behind here but I don't think it's likely and I think given the fact that its a limped pot, checking here and giving the table an opportunity for a free card when so many of them can hurt me is a mistake.)

Fold,
Villain calls
folds around

Turn (12bb):7s5c3c3h
I bet out 7bb. Not really sure how I feel about my sizing but I know that I'm almost definitely not folding. I think 88 and 99 are possible but it's still very likely that I have the best hand. Sure, he could have A3 but it's much more likely that he's got a weaker pair or a draw with some equity that he would like to see through. Even if he raised here, which I think could be pretty likely, I don't think I would fold.

Villain calls.

River (26bb): 7s5c3c3h4d
Here I check, I don't think many weaker hands will call. I might get a call from Q7, 66 or A5 exactly but I'd rather just get a cheap showdown and not get raised here. A2, A6, 76, 65 all just got there.
Villain bets 4bb
Given the pot odds here I think we have to call, but I don't really understand the effect this bet has on his range. I feel it has to be heavily weighted towards the bluff/thin value bet area. He's called twice now so likely has something but very well may feel he can't win unless I fold, but also doesn't want to risk very many chips. It's a pretty scary board for my hand but I just find it very difficult for him to have a value hand here after limping UTG+1, is he really doing that with 54, 43? He could absolutely be slow playing a boat but I think I would have heard about a 3 or a straight by now.