Preflop
($0.15) Hero is SB with 4s Ah
2 folds, Hero raises to $0.30, UTG calls $0.20

Confused HH import haha

Anyway, as you said this is a BvB spot.
If so, as played, I don't mind to check-call river.
Ranges are too wide in BvB spots, you'll see people value betting worse hands, bluffing missed draws, random bluffs, etc. It would be diferent if ranges were way tighter.

About the flop I don't think that will be a huge difference between checking or betting but you must emember to include bluffs when you decide to Cbet value. Personally I prefer to check a lot in BvB spots when I'm the SB preflop aggressor.

On the flop betting small or checking are valid options, as Mancuso said it's more about your overall strategy.

In theory you should be calling down your top pair unless you know that your opponent is overbluffing when he 3-barrels here. You unblock clubs and most of his straight draws (blocking 54 and 64) and block his most likely value, so it's a good call if you are playing a robust strategy.

The population probably underbluffs here and I suspect A-high boards aren't the more bluffed, but I'm not sure. I'd call top pair or better until I have better reads.

Agreed with the other posts above. Flop and Turn are standard. Call river. You block value and unblock bluffs - which is exactly what you want in a bluff-catching scenario.

Looking to bluffcatch river, for the reason David Alford mention.
About the flop strategy either cbet or check is fine with ur hand, depend what your strategy is. I tend to check the weak Ax if i play a checking range in this spot. I lean towards almost rangebetting this texture tho because it favours SB so much.