Small low stakes home game tourney
14 players started - down to 4 at final table
Top Five recieve at least rebuy for prize
Blinds are .25/.50

Intersting hand
Hero has A4
Pre-flop
Hero calls BB, Button folds, SB calls BB, BB checks

Flop - 3bb
A7A
Sb bets 1.00, BB raises to 2.00, Hero raises to 6.00, Sb calls,BB raises to all-in, Hero thinks then folds, SB folds

My read on BB was that he had at least A-10 and I was beat. This was after he raised all-in. After the hand I found out that BB did indeed have AK.
SB had around $50, BB had $20 and Hero had $18.00

Is this an alright fold on my part? What would you do in this situation?