Well I think you have two options (or you can combine the options into one).
Firstly, you could work your weak arm by itself to improve its strength to kind of get it to "catch-up" with your stronger arm. By this, I mean some dumbell exercises or something.
Or, you could do as you say -- do curls or something until your weak arm can't take it anymore.
Really I don't even think you'll have to worry about it much to get it to correct itself.
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