[BarryLyndon]

Meh, it's fine, and on all streets. He could be doing this with a busted flush draw sensing weakness on your behalf; his aggro factor is high enough and that wouldn't be "out of line." He might be doing this with AQ, sure, he doesn't want to get blown off the hand and he feels he has equity off of AJ or even KK. The 2nd four helps you as you can more realistically eliminate 44 from his range. 22 you can eliminate too, so you're really only worried about 77 here. Or maybe AA, but you have one of the As, so once again, a little less probable.

If you felt confident about his calling/folding tendencies to narrow his range to AQ or AJ, you could try repopping on the River, as he's already built a pot to feel committed with AQ, AJ, etc., and may feel like you missed your flush draw (as you played it). So that has potentially more value, but with more information (I feel).

Edit: What makes calling > reraising here is, as cs points out, the structured betting here, which indicates strength. However, I think the possibility of such betting with AQ/AJ/perhaps a flush draw on this particular board (an A with the rest being lows and no connectors) makes calling +EV and I don't think you can fold.