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Villain is playing 21/13 FCB:87 ATS:24 AF:1.7 over 482hands.

Full Tilt Poker $0.10/$0.25 No Limit Hold'em - 5 players
The Official DeucesCracked.com Hand History Converter

BB: $39.11
UTG: $34.50
CO: $20.54
Hero (BTN): $34.54
SB: $25.50

Pre Flop: ($0.35) Hero is BTN with 3 3
UTG raises to $0.75, 1 fold, Hero calls $0.75, 2 folds

Flop: ($1.85) 3 7 Q (2 players)
UTG checks, Hero bets $1, UTG calls $1

Turn: ($3.85) J (2 players)
UTG checks, Hero bets $2.25, UTG calls $2.25

River: ($8.35) T (2 players)
UTG checks, Hero bets $4.25, UTG raises to $30.50 all in, Hero requests TIME ?

CR on river is almost always the nuts.
but i think you can beat a range cr range. if he is doing it with 2 pair, qj, qt.
I really think you have to call and say it is cooler if he shows you the nuts.

Flop and turn bets look way small to my eye.

Flop bet is sized well imo. You will bet this flop 100% when checked to, so you want to get away with the smallest possible bluffs. But after he calls the flop, I would bomb on the turn. We have to build the pot, plus there are two face cards on the board, which is likely to hit his utg range. Also, bet a lot bigger on the river.
I think villain shows up with JJ/TT/or even QQ on the river a lot. The only two pair hand he can have is QJ, but even that is doubtful, he is 21/13.
We should make a really nitty fold, but I doubt I could do that in game. It would feel very weak as we have the top of our range, and only a few combos beat us, and villain took such a strange line, there is a spazz factor involved.

This is an interesting hand. The crux of it, imo, is why wouldn't he cbet this flop?

Just judging from his stats I'm going to assume that he's the sort of person who doesn't cbet without the goods, rather than the sort who would be checking sets/TPGK/overpairs to induce (which sounds like a stretch over 3 streets anyway). Consequently, I'm guessing he shows up here with TT or perhaps exactly AK a lot. I'm probably too big a station to not call anyway.

Also, I'm not sure this:

Flop bet is sized well imo. You will bet this flop 100% when checked to, so you want to get away with the smallest possible bluffs.

... really matters? We can probably get away with any sizing we want to if he's checking to us as the PFR a lot, and adjust some part of our strategy when he starts doing it to do something besides folding (if ever), with sizing only being one element we can adjust.

Flop size is fine due to the dry board texture. Bet bigger on the turn though. Also bet bigger on river.

Doubtful villain check/calls flop and river with AK/KT, so villain almost never has a straight. He also probably bets flop with 98. This is most likely a two pair hand like QJ/QT or a better set.

Against a range of KQ, QQ, JJ, TT, 77, QTs, QJs this is a pretty easy call. Take out KQ and any other weirdly played one pair hands, like AA/KK and it's a fold. I would assume however that villain will show up with enough one pair hands to make calling correct. We can also discount at least some combos of sets, because he may not play them this way.

Guys AF is really low. A cbet stat would be nice, but seeing AK wouldn't shock me here. I'd expect to see that more often that QJ or QT. I'd fold the river personally.

Agree with comments about flop bet size being fine, but once he shows interest betting close to pot on the turn.

i still think we can and should bet bigger on the flop. Big bets early generate much bigger bets later. Just because we bet big here doesn't mean we have to bet like this with AQ, 56, Ax, 88 or anything else, and I really think that unless we are very obvious about it and play way too many hands against not terrible looking villains, we wont be tipping our hands. And a big bet on a dry flop looks bluffy trying to buy the pot, i think, a lot.

Also, the logic of bet small flop bomb turn makes no sense to me. Are people are saying to bet the flop small to keep marginal hands in, but then bomnb the turn because the flop call shows he has a hand he likes? You can't have it both ways. If a call indicates a good hand, we should bet big, if he'll call smaller bets with marginal hands, then bombing the turn sounds wrong.

Bottom line, big hand big pot. It's a dry board with only one high card, so you can expect villains to call 1 bet with a fair range of hands, and I expect such ranges to be pretty inelastic.

I agree that we can think about a nitty fold here. I'm not sure I could make it at the table, but i think it's hard to find worse hands he does this with, unless he could do it with AA

I like smaller bets personally so I don't have a problem with the bet sizing except I might make it $3 on the turn. River sucks but it's a fold because he's never bluffing here and he's not playing KK+ like this and that's all you beat.