There's an error of 1 lb or more both for your scale and theirs. If it really reads 52 lbs they might let you go: they let me check a 72 lb suitcase one time.

But if a reading of 52 on your scale means 53 actual weight and 54 on AA's scale, that won't pass. In other words, it's a good idea not to be confident that your scale is giving you the highest possible number.