PokerStars No-Limit Hold'em, $0.50 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

UTG ($30.25)
Hero ($55.90)
MP1 ($48.45)
MP2 ($44.85)
MP3 ($79.15)
CO ($25.30)
Button ($47.75)
SB ($9.50)
BB ($51.35)

Preflop: Hero is UTG+1 with Q, Q.
1 fold, Hero raises to $2, MP1 calls $2, 6 folds.

Flop: ($4.75) 8, K, 6 (2 players)
Hero bets $3.5, MP1 calls $3.50.

Turn: ($11.75) 6 (2 players)
Hero checks, MP1 bets $7, Hero folds.

Final Pot: $18.75

MP1 is super-tight. I have 3.5k Hands of him playing 9/1.
He is coldcalling less than 1% (26 out of 3481) and folding 75% to a c-bet (57 out of 71).
My thoughts in white below:
I don't think there is any hand he is CCing AND calling the C-bet with that I can beat. Unfortunately I have no notes what he is CCing with, but I think he sometimes calls AA and KK to trap me and AK, AQs and 22+ to see the flop. So I think he has either a set or Kings+. There might be a small chance he has QQ or JJ and doesn't want to give it up for one bet.

Do you think this play was to weak? Should I have bet the turn, folding to a raise? And what to do if he flatcalls the turn, too?