Villain is 14/11 over 248 hands. I didn't bet flop because I wasn't sure what else worse would be calling aside from 88.

PokerStars - $0.05 NL (6 max) - Holdem - 5 players
Hand converted by PokerTracker 3

SB: $1.95
BB: $2.96
Hero (UTG): $5.02
CO: $2.00
BTN: $2.50

SB posts SB $0.02, BB posts BB $0.05

Pre Flop: ($0.07) Hero has 9 9

Hero raises to $0.20, fold, BTN calls $0.20, fold, fold

Flop: ($0.47, 2 players) 7 7 J
Hero checks, BTN bets $0.25, Hero calls $0.25

Turn: ($0.97, 2 players) 2
Hero checks, BTN bets $0.50, Hero ????

I don't think you have given nearly enough information to assign the villain a range here (especially when you have about 250 hands on him). Three questions: How often is villain 3betting, how often is he cold-calling preflop, and what is his fold to cbet percentage?

If he is 3betting 5-6% or so, that is 99+, AJs+ and AQ+. Assuming he doesn't ever limp (which seems likely for a 14/11 nit), a 3%-ish calling range is probably something like 88-55, JTs-76s.* In this case, I think you should value bet the flop, since he is unlikely to have an overpair and you might collect a bet from a weaker pair on a flop like this (from his perspective, you probably have high cards that likely missed this flop, though he will be wary about an overpair). I don't know what giving him a card here accomplishes. If he is unlikely to call you on the flop with an underpair, he's not likely to do so on the turn after another card comes - an overcard makes the board scarier to him and an undercard (or a spade) just might let him catch up a little more than you'd like (it's not like you have a dominating hand).

*Since he is on the button, his cold calling range may be wider, but that only helps you, as it adds more lower pairs to his range.

If he is 3betting only 3-4% or something similarly nitty, you need to check his cold-calling percentages (the standard PTR HUD set-up will have this as a pop-up). If it is something nitty like 3%, you have to be worried about overpairs. Now his 3% calling percentage looks more like JJ-77, JTs-76s. You are a 2:1 underdog against this range after the flop. Depending upon his fold to cbet percentage, I would mostly c-bet to represent an overpair, but a check/fold seems doable against such a nitty villain. If he has a wider cold-call on the button with something like 6%, I think your cbet becomes standard again, since more small pairs go into his range. Moreover, when you check, you are pretty much inviting a TAG to put in a bet.

On the flop, he could be value betting a pair, semi-bluffing a flush draw and/or trying to push you off your hand (which probably looks like missed overcards). Once he double-barrels the turn, I'm not sure what to do after a check-call on the flop.

I guess that, as played (and without any post-flop stats), I probably fold here to a double-barrel from an nitty villain, though it depends on how aggressive I have seen him play post-flop. Either way, if you call, you are probably going to be faced with an unpleasant decision on the river.