Villain is 17/14/inf agression over 71 hands.

What do we do? And what is/was the best play?

PokerStars - $0.10 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

Hero (BTN): 136.7 BB
SB: 75.2 BB
BB: 87.9 BB
UTG: 227.1 BB
MP: 100.5 BB
CO: 111.4 BB

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has 7 7

UTG raises to 2.8 BB, fold, CO calls 2.8 BB, Hero calls 2.8 BB, fold, fold

Flop: (9.9 BB, 3 players) 6 4 2
UTG bets 3 BB, fold, Hero calls 3 BB

Turn: (15.9 BB, 2 players) 7
UTG bets 13 BB, Hero raises to 30 BB, UTG raises to 51 BB, Hero calls 21 BB

River: (117.9 BB, 2 players) K
UTG bets 82.2 BB, Hero

I'd just call the turn here. You have a strong hand with a pretty decent chance to improve otr. But, both you and villain should have a lot of flushes in range, so I don't think a set is high enough in your range to warrant a raise. It would be different with say 77 on a AK7 monotone board, as the flop considerably decreases the number of possible flushes both players can have, so the set would be further up your range.

My personal view, and it may well either be wrong or oversimplified, is that monotone boards should be played more cautiously. So, less value bets, lower sizings. Once you get to the river, you're in a horrible spot. I think a fold might actually be a good idea. You have blockers to 8d7d and Ad7d, but I'm not sure that's enough to call. AdAx I think would be a much better call, as would KdKx, and maybe even QdQx. Although I'd imagine you're not getting here with them. Then all pp with a d down to 88 (8d8x blocks 3 possible value hands), because like your hand, they beat the bluffs, but have better blockers. Considering what hands you have that would want to take this line Otr, I think 77 is probably your weakest value hand, so I'd tend to fold due to that.

don't raise turn for value w/o a flush