Can You Lay Down A Set?

Maybe this is results oriented, but I really feel this is a time where you can lay down a set. Villain was a tight player (13% VPIP) so what the heck can he have here other than 77 or TT? I tried to convince myself that he could have AKdd or something, but mainly my logic was that you can never lay down a set. Don't think that's true anymore. A tight player will not overplay an overpair in this fashion. Well, usually not.

$0.5/$1 No Limit Holdem
9 players
Converted at weaktight.com


Stacks:

UTG		($196.15)
UTG+1		($19.00)
MP1		($20.85)
MP2		($117.00)
Hero		($113.55)
CO		($76.80)
BTN		($19.60)
SB		($52.00)
BB		($98.50)

Pre-flop: ($1.5, 9 players) Hero is MP3

4 folds, Hero raises to $4, 1 fold, BTN calls $4, 1 fold, BB calls $3

Flop: ($12.5, 3 players)
BB bets $8.5, Hero raises to $20, 1 fold, BB raises to $50, Hero goes all-in $109.55, BB goes all-in $44.5

Turn: ($201.5, 2 players)

River: ($201.5, 2 players)

Final Pot: $201.50
BB shows:
Hero shows:

BB wins $198.5 ( won +$100 )
Hero wins $15.05 ( lost -$98.5 )
BTN lost -$4.00