I am not more ugly than your sister.
Does this mean I am as ugly as your sister?
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As oerlekens says, it means that the speaker's ugliness is less than or equal to that of your sister.
It's an unusual comparison to make. I suppose if the other person had just said, "Wow, you're even uglier than my sister", this would be a response that makes sense.
A more common phrasing would be, "I am not as ugly as your sister" or "I am less ugly than your sister."
As such a statement clearly implies that the other person's sister is ugly, and that would generally be a very rude thing to say, any sentence like this would be rare. I'm hard pressed to think of a context where someone would say this other than trading insults. Like, "Wow, you're really ugly!" "Well, at least I'm not as ugly as your sister!" "And you're stupid too!" Etc.
The "not more than" phrasing may be a careful choice of words intended to imply "less than" while allowing for the possibility of "equal to". It reminds me of a commercial for a headache medicine I once heard where they said, "No pain reliever on the market is better for your headache than [our brand]". If you don't think too carefully it sounds like it's saying that theirs is better than all the others. But all they really said is that no other is better than theirs. It led me to wonder if in fact all the headache medicines on the market may in fact have exactly the same active ingredients, and so they are all just as good. So the manufacturer says "No one else's is better than ours", it sounds like they mean "ours is the best" when really they are just saying "they're all the same".