Winning Poker Network (Yatahay) - 4,000/8,000 NL - Holdem - 4 players
Hand converted by PokerTracker 4: http://www.pokertracker.com

SB: 17.67 BB (VPIP: 23.53, PFR: 20.00, 3Bet Preflop: 11.43, Hands: 85)
Hero (BB): 24.84 BB
CO: 27.58 BB (VPIP: 5.66, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 53)
BTN: 84.91 BB (VPIP: 38.46, PFR: 37.50, 3Bet Preflop: 33.33, Hands: 53)

4 players post ante of 0.1 BB, SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 1.9 BB) Hero has 6h Ts
fold, BTN raises to 2 BB, fold, Hero calls 1 BB

Flop : (4.9 BB, 2 players) 9h Td 7c
Hero checks, BTN bets 3.27 BB, Hero raises to 8.5 BB, BTN raises to 82.81 BB and is all-in, Hero calls 14.24 BB and is all-in

In this spot, Villain had been RFI a ton at the FT and running it over. I had played back once or twice and had defended BB and check folded flop several times. Every time villain went to showdown or got all in pre they had the goods, but it seemed like a FT where villain may have been just running really good in terms of preflop card distribution and happened to get 3b a lot when they had it. One spot when we were 6-7 handed I 3bet piled like 15bb in BB with KJo and they snap called K9o.

My question is- is this flop spot better as a check/call or easily a better check/shove?