Should i have checked behind or right to value bet river?

Swog

After calling a big bet on the flop then checking the final two streets OOP i didn't put him on either a King or a Flush, thought he had a smaller Ace, which he most probably would of called a small value bet on the river.

I just couldn't see him playing a flush or a King like this, was my fold the correct play to his big check raise on the river?

nffc4eva	Small blind		£0.02	£0.02	£3.15
bbb10	Big blind		£0.04	£0.06	£3.79
	Your hole cards	A Q
tracey1969	Fold
winsawin09	Call		£0.04	£0.10	£3.72
Swog	Raise		£0.20	£0.30	£6.35
nffc4eva	Fold
bbb10	Call		£0.16	£0.46	£3.63
winsawin09	Fold
Flop
		A K 7
bbb10	Check
Swog	Bet		£0.35	£0.81	£6.00
bbb10	Call		£0.35	£1.16	£3.28
Turn
		K
bbb10	Check
Swog	Check
River
		3
bbb10	Check
Swog	Bet		£0.44	£1.60	£5.56
bbb10	Raise		£1.97	£3.57	£1.31
Swog	Fold
bbb10	Muck
bbb10	Win		£1.88		£3.19
bbb10	Return		£1.53	£0.16	£4.72

rancid

bet turn
b/f river

beaneh

river bet is fine you can check if you have no idea on the player but I would assume they are not bluffing the river so it is an easy bet fold.