The hand plays "easier" here for lots of reasons if you bet...

But I think the optimal play is to check.

In a reraised pot we're not generally worried about suited cards.

Betting pushes out JJ/1010/99, all hands that could potentially put us on whiffed big cards (think AQs or something) that missed the flop.

I've gotten paid off for 1 bet and sometimes 2 by lower PP's by taking the check flop - bet turn line.

If villain is super aggro and likes to push you off hands then I can uderstand the bet (since it'll be hard to wrestle the pot away from him on later streets and he'll be likely to pump the flop)...

In this particular spot, I'd check-call flop and check-fold or cr/ai turn almost always, prob something like 50/50 frequency. Also, you might think about 4-betting/pushing depending on how loose the Btn has been 3-betting.