Opp has taggy stats over a larger sample size, and seems solid. First time i 3-bet at this table. Line check please?

My thoughts on the hand: I feel my hand is very transparent by the river, if he is able to read hands he can put me squarely on JJ/QQ - how should I play this against someone who's solid? I feel if I bet somewhere here I turn my hand into a bluff basicly, which is bad because my hand has showdown value. Also, his preflop call of my big reraise was really suspicious, if he is as solid as I think he is, then I probably put him on AA/KK/AK (or QQ, but the chances of that are small).

Party Poker No-Limit Hold'em, $ BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

UTG ($114.04)
MP ($115.74)
CO ($40)
Button ($98.35)
Hero ($260.57)
BB ($112.68)

Preflop: Hero is SB with Q, Q. Hero posts a blind of $0.50.
UTG calls $1, MP calls $1, 1 fold, Button raises to $6, Hero (poster) raises to $17.5, 1 fold, UTG folds, MP folds, Button calls $12.

Flop: ($39) T, 6, K (2 players)
Hero checks, Button checks.

Turn: ($39) 5 (2 players)
Hero checks, Button bets $25, Hero calls $25.

River: ($89) 7 (2 players)
Hero checks, Hero folds.

Final Pot: $89