In this hand the BB is a regular that I have played about 100 hands with. When I raise in the SB I expect the BB to call with a wide range of hands, probably at least his top 30%. I go ahead and bet the flop for value. I would probably check fold on this flop with weak hands like A4o or K8s.

When I get raised, it reps an extremely narrow value range. It represents 33, 77, 99, and 97s, which is a total of 1.5% of preflop starting hands not even counting card removal. It's also possible he is raising a made hand like TT or A9 but it seems natural to call with those hands on the flop. A raise could also be a semibluff with a straight draw like 8T or 86. It is quite likely my opponent would attack me on this board because it looks like it doesn't hit my range. If I 3-bet the flop I can represent a lot of strong hands - 33, 77, 99, 97s, QQ, KK, and AA. With my bet sizing I am risking $21 to win $22, so I am counting on my opponent bluffing at least half the time. I consider this a better option than flatting because there are a lot of turn cards that could come that I wouldn't like, any 6,8,T,J,Q, or K.

nice analysis. are you calling a 4bet shove or folding to a shove?

I would fold to a shove; essentially this is a semibluff. It is possible but unlikely that he has a set, and it is unlikely that he would risk the other $85 in his stack to win $43 as a bluff, especially since there are a decent amount of hands in my range I could call with.