You did show weakness by checking the turn. You are getting 2.5 to 1 pot odds, so you would have to be fairly sure the opponent has A2XX to make the fold. If you think the opponent is making a move on you, calling would not be that bad a move. Against a hand such as KKXX or QQXX, you are getting good odds to call (3 to 2 odds).

The only reason I would consider folding is the raise preflop usually means A2XX or AAXX, and from his play on the flop I do not think villain has AAXX. And you are just not getting proper odds to draw against A2XX with a better high hand.