Don't know what you mean by IP?
A2 unsuited from CO is marginal.
This would really depend on if you had been abusing the blinds from the CO and you think SB is just making a stand.
On the flop SB led out with 1/2 pot bet rather than check to the preflop aggressor. To me that looks like:
a pair of queens or weak ace wanting to find out if they are good
on big hand and building a pot
it is not a stab at the pot hoping for you to fold or they would have
bet more
You bet 20 into the pot bringing it to 35. SB is getting 35 : 15 to call.
What are you trying to do here? Are you trying to get a single pair to call for value? 20 is 1/3 of your stack on the flop - you are pot committed with that bet.
SB pushes so you are getting 90 : 40 to call
What can you beat?
What can you loose to?
AQ
yes villain would have played it that way
AA
you hold and Ace so not likely and they would slow play that
and probably would have raised preflop
QQ
not likely as they would slow play that
and probably would have raised preflop
Lone Ace
Even a lone ace will beat you 17% of the time as even a paired board counterfeits your pair of 2.
Without a read on them I guess you need to call. You are basically pot committed. You are probably beat but you are getting over 2 : 1. If you fold you are down to 40 bb but 40 bb is still playable.
Back to why raise the flop. If you are ahead then you will likely stay ahead as there are no draws on the board. If the plan is to get their chips then let them bet into you. You have position so you can always bet if they check. If they then bet the pot on the turn which they likely would then you would have decision to make.