I absolutely adore Asami, she's just an incredibly well designed and well written character.
It makes sense that Asami would look more 'weathered' than her daughter, because as any decent mother would tell you, You would do anything to protect your daughter even if it means enduring everything yourself, which is what Asami has done, and it shows, she may be 'ugly by your definition' but that does not mean that everyone is going to agree with you. Opinions are like assholes, everyone has one and they usually stink.
Not knowing what you yourself or anyone has been through personally I cannot say the following with confidence:
You try going through everything Asami has had to face in her life without any help and then suddenly you find someone who not only treats your daughter with a level of kindness the likes of which you have never seen before, but then they eventually extend the same kindness to you asking for nothing in return (While you know deep inside that everything you've done or given in the past has always had a cost).
You go through all of that and tell me you would not show any signs of wear and tear both physically and mentally.
Whether it's scars of wrinkles, they can be sexy and they can portray more of a story into someone's life than actual words can.