Tricky button/bb situation (10/20)

[sam h]

It is folded to player A who raises on the button with J9o. The mediocre SB calls and Player B, a very tough aggressive player, calls in the BB. Player A knows player B pretty well, and Player B knows player A at least well enough to know that his opening range here is wide.

Flop is 4d 3d 2s. It's checked to Player A who bets. The SB folds.

First question: What percentage of his hands should Player B be checkraising here?

Turn comes an offsuit 2.

Second question: If player B checkraises a lot here, how often should player A "defend" (by three betting the flop or raising turn) with hands that don't have much showdown value (ie - no pair, no ace)? What is the thought process for thinking about when to do this and when not?