.05/.1 Limp button with 53s? Cap flop?

[FineStyle]

I don't play short-handed, I would call that with a couple of bets before me long-handed in the button. This is a highly speculative hand.
I would just call the 3-bet on the flop. The turn check is fine, you got your free card so take it. If these are weak-passive players you might bet to take the pot right there, but BB might raise if this is not the case.
The river is a fold. You have nothing.