NL10 - Medium overpair facing heavy post-flop pressure after 3-bet pre-flop

I was involved in the following hand which presented a tough decision on the turn.
Villain on button was quite TAG (VP:16 / PFR:10.8 / 3B:5 / CB:79 / AF:2).

PokerStars - $0.10 NL - Holdem - 8 players
Hand converted by PokerTracker 4

BB: 71.5 BB (VPIP: 18.18, PFR: 14.09, 3Bet Preflop: 10.23, Hands: 225)
Hero (UTG): 94.1 BB
UTG+1: 106.8 BB (VPIP: 24.19, PFR: 14.52, 3Bet Preflop: 8.33, Hands: 127)
MP: 100 BB (VPIP: 23.13, PFR: 6.56, 3Bet Preflop: 2.32, Hands: 880)
MP+1: 127 BB (VPIP: 28.33, PFR: 5.83, 3Bet Preflop: 0.00, Hands: 122)
CO: 154.7 BB (VPIP: 14.97, PFR: 13.61, 3Bet Preflop: 8.15, Hands: 449)
BTN: 118.9 BB (VPIP: 16.37, PFR: 10.85, 3Bet Preflop: 4.80, Hands: 571)
SB: 109.7 BB (VPIP: 16.20, PFR: 14.08, 3Bet Preflop: 7.89, Hands: 146)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has 9♦ 9♥

Hero raises to 3 BB, fold, fold, MP+1 calls 3 BB, fold, BTN raises to 12 BB, fold, fold, Hero calls 9 BB, MP+1 calls 9 BB

Flop: (37.5 BB, 3 players) 4♣ 5♠ 8♣
Hero checks, MP+1 checks, BTN bets 14.7 BB, Hero calls 14.7 BB, fold

Turn: (66.9 BB, 2 players) T♣
Hero checks, BTN bets 31.8 BB, fold

BTN wins 63.6 BB

Replay

What do you think? Fold or continue?