PREFLOP: For me to consider raising with a garbage hand like A7o, there are a few key variables that have be in place.

1) The button, small blind and the big blind have to all be very tight players, the kind that are very unlikey to call my raise. I find that the probabilty of three players all staying out of your way in this spot is usually very low, and this is essential component to your strategy since if one of the players behind you calls then you will usally have to make a hand to win, and A7o doesnt make a hand very often(you only have 3 outs to a hand basically)

2) The opponent you are isolating must be the type that really repects your raises or other peoples raises in general making him unlikely to chase that much postflop in this situation. Again, this is a critical aspect to your strategy since most of the time you are going to miss the flop pretty badly and you can find yourself just bluffing your chips off with 3 outs or less. I believe most opponents of this description will play too loose postflop, not too tight, which is exactly what you dont want.

3) Another important factor is how predictable your opponent plays postflop, if he is tricky at all and will put pressure plays on you, then raising with a hand like A7o is just not worth the trouble since most of the time you wont have a hand that can combat his trickiness.

So to conclude, to make the play you are attempting, these 3 variables must be in place in order for your isolation strategy to be +ev IMO, And I suspect that isnt the case in your hand.

One more thing, I would fold the flop, the pot isnt that big, you have no hand, the gig is up. When you have no hand, and your caught, there is no need to tough it out, just fold. There are alot of very aggressive people on partypoker, where calling down with ace high is a very profitable strategy, but I dont think this opponent is that aggressive postflop. When he bets into you with the BB also in the hand, I believe he's got something, even if he has only a flushdraw which is your best case scenario he still has 15 outs and 2 streets to hit which means he will still overtake you 54% of the time. So even in your best case scenario, you are still an underdog.