if you have made up your mind to play this after the flop i think you should push all in. why call for half your stack you are then commiting yourself anyway. your read was good on the guy who led out on the flop he might of passed his AK but if it was folded back round to him im not sure he would but you would of had 14 outs against him. obviously you dont know for sure that 6 of them are live.
you call in these stacks because you have no reason to stick the rest of it in. There are typically two reasons why people shove their stack in:
a) to get value out of the best hand
b) to make people fold
When Mr AK bets 500.. our hero has 500 left.. how often do you think he is going to fold AK in that spot...the answer is pretty close to zero..so that makes point b) invalid.. and at the moment we are stuck with 7 high, so that makes point a) invalid as well.. so you should just be calling here if you intend to play the hand.
The thrust behind this thinking in a nutshell is that you get paid 100% of the time when you hit, and you need to hit to win obviously, so calling down is preferable to moving in because :
When you call down instead of moving in.. you win the same amount of chips as if you move in, but sometimes you get a free turn and are still in the tourney if you miss... so you win the same as jamming when you hit, but you dont ALWAYS lose the same when you miss, which is a pretty good spot to be in**
** of course it doesn't always work like this, there are no absolutes in poker, but this is the general premise behind why you do it
Its possible that by raising you can possibly get your 4 and 7 to become clean outs, but its also the case that if someone behind you has better then a pair of sevens, he isn't folding anyways, so it goes back to the point of not getting hands out that you really want to go out, and stopping others coming along for the ride (which wouldn't be bad at all with your draw.. getting overcallers and exceptional value on your $ in these spots is always nice)