5-Card Draw: Limping Villain

[Biggle10]

Occasionally when playing draw, I run into a player who never raises and then will draw 2 most every time. Villain does this with both trips and small pair w/Ace.

I have a hard time after the draw value betting anything less than trips against this kind of player. Should I even be trying? I hate checking behind when I make KK up, but that seems like right choice most of the time.

Anyone have experience with this kind of opponent?