TPTK on a paired board vs. a tricky player

[Mr. Curious]

300-500 live NL game
9 handed
Blinds are 5/10
Maximum bet is $500 (state law)

Stacks:
Hero $825
MP2 $850
BB $2000

Hero is on the button with AJo

Preflop:
UTG folds, UTG+1 folds, MP1 folds, MP2 calls, MP3 folds, CO folds, Hero bets $40, SB folds, BB calls, MP2 calls

BB is defending his blind and calling because he has a huge stack and has been getting some decent flops. His hand range is quite large, though he would have re-raised preflop with AK or AQ, AA-TT.

MP2 is a tight, aggressive, tricky player. His calling hand range is any pair, any suited connecter, any suited ace. He would have open raised with AA-99 + AK/AQ, though he might have tried for a limp reraise with AA or KK. He will try to push people off their hands and has already check raised with top pair against a preflop raiser's continuation bet.

Flop: J77 rainbow (3 players)
Pot: $120

BB checks, MP2 checks, Hero bets $100, SB folds, MP2 raises to $200, Hero raises to $400, MP2 pushes all-in, Hero calls