Getting called on a paired flop

Villain was 35/11 and cold-called a lot over a few hundred.  I haven't been at the table that long, no history.

Full Tilt Poker $0.50/$1 No Limit Hold'em - 6 players
The Official DeucesCracked.com Hand History Converter

SB: $100.50
BB: $83.80
UTG: $209.35
MP: $28.70
Hero (CO): $100.00
BTN: $34.50

Pre Flop: ($1.50) Hero is CO with Th Tc
2 folds, Hero raises to $3.50, BTN calls $3.50, SB calls $3, 1 fold

Flop: ($11.50) 8d 8s 2d (3 players)
SB checks, Hero bets $7, BTN calls $7, SB folds

Turn: ($25.50) 4c (2 players)
Hero bets $25.50, BTN says "hmmmm", BTN calls $24 all in

River: ($73.50) 5d (2 players - 1 is all in)

Final Pot: $73.50
Hero shows Th Tc (two pair, Tens and Eights)
BTN shows 8h 8c (four of a kind, Eights)
BTN wins $70.50
(Rake: $3.00)

The guy seems like a bit of a drooler, so what is his range when he calls the flop?  Of course he could have an 8, but I think we also should give him overcards and flush draws.  However, on such a dry flop, a call from him is pretty scary, or would be if we were full stacked.

Let's assume he's not floating that often, so he's likely to check behind if he's behind (and also sometimes if he's ahead, so he can cleverly trap me on the river).  But if I make a big bet on the turn and he calls, I'm almost definitely screwed.  At the time, I think I was thinking that if no more money was going to go in from him unless he pulled ahead of me, I might as well go ahead and bet to make him either make a mistake or sacrifice his pot equity by folding.  And since the stacks were so short (pot-size bet left), any bet might as well just be a shove.

I'm not sure that's a huge mistake given how little we have behind, as I think I do want to bet.  But, by making a pot-sized shove, I'm pretty much assuring that I don't get called by worse, and here no better hand is ever folding.  His flop call means that he's likely got 6-12 outs when behind, and I think that I want to make a bet here that encourages the top part of his range to make a mistake by calling, given I don't think I can induce a bluff now or a bad call on the river by checking the turn.  So, maybe making a $15 bet into $25.50 would be better.  I still get to protect my pot equity, but now I might also get some more worse hands to call.  True, for some of them, he might call anyway to a PSB, but probably only his very best hands that are behind me.

The other option is to check, and that might be for the best here, under the assumption that he didn't call the flop with the intention to float me (he just called because he calls a lot)...but even though that might not be his intention, I think the temptation to float would be pretty high if he ended up with the opportunity, yet a check/call on the turn seems bad too.

So, what do you guys do with so little behind?