AKo lots of action preflop

Live game, $20NL, .25/50 blinds
Hero has about $16
Main villain has about $25

Reads on villain:
Villain is a regular who loses at the table a lot. He can't let go of semi-big hands, and usually doesn't steal too much. Usually plays it a little cautious.

Villain has JUST sat down for about 5-10min

MP1 is a terrible player and will play with any 2 cards. Not concerned about him.

Hero is dealt A[img]/images/graemlins/club.gif[/img]K[img]/images/graemlins/spade.gif[/img] UTG

Hero raises to $2.00
MP1 calls
Villain calls
BB re-raises to $4
Hero calls
MP1 calls
Villain pushes all-in
BB folds

Hero.. ???

So, the pot is about $13 + villains all in.

I have about $12-13 left in my stack. Essentially, I'd be calling a $13 into an essential pot of $26, giving me about 1:2.

I laid this down, but am now thinking I should have called with the pot size. Thoughts?

If I assume villain has a pocket pair like QQ, JJ, etc - is this a profitable call?