Preflop
I dont really see the need for 3-betting this hand from BB and especially not at 2NL. Its very aggressive, and at this limit people tend to not fold very much to 3-bets. In which case you have just bloated the pot out of position. I would just call here and see a flop.
Flop
I would play this hand as a check-call. I dont really see, what the bet does? Better hands either call or raise, and most worse hands fold. If on the other hand you check and let him bet, then he can have bluffs in his range, and you have way more equity going to the turn. He might also check back, which is a totally fine outcome.
Turn
Now I understand even less, why you are betting? Are you trying to get him to fold trips? That will never happen. Or are you trying to get called by hands like 55-TT? That is probably also not going to happen, unless he is a total whale.
River
You painted yourself into a corner, and now you have no other option than to check and fold.
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