I have a super cute kid too. He is very tiny for his age, has olive skin, BIG blue or sometimes green eyes, and crazy curly hair. And EVERY. SINGLE. TIME. we leave the house I get compliments on his looks especially his eyes and or hair. (oh look at those eyes/hair, he is beautiful, he is too pretty to be a boy, oh he is so cute, does he do modeling? etc.), and its said directly to him, to me and sometimes just to someone else (I hear people telling each other "did you see that little girl? she is so pretty" - talking about my son!)
My son has done 2 modeling things - one was to help a friend with his portpholio, and the other was to do the ad's for our local zoo. We were asked by the zoo director to come in for the photoshoot because we are there so often. Her reason for choosing Levi? Because he has a good personality and follows directions well and because he is so happy all the time - nothing about how cute he is! We love that zoo so Im happy to promote it, and Levi got to hold/pet animals he doesnt usually get to so it was just fun for him!
But yeah I agree the compliments do get anoying. Its been happening sense he was tiny! He even seems de-sensitized to it, because he just says "yeah I know" now (I have to remind him to just say "thank you", he says that for everything else, I think he is just 'over' being complimented so often)
But at the same time, you have to look at people's intent. Their idea isn't generally to 'value' his looks over his other qualities, BUT, they havent 'met' him yet or really talked to him, the looks are just what people see at first glance, and often they 'react' to that with a comment because he IS really 'pretty'. Many times these comments from people are just said in passing (walking by, in line at the store, from the next table out to eat, etc), but the times where people have actually started talking to my son, they also end up complimenting on how smart he is, how well he converses with adults, how big his vocabulary is, how funny he is, how polite he is, how well he can follow directions, etc. And that usually ends up being far more 'impressive' to people than their initial opinion of his good looks.
With a cute kid, you are going to get comments, thats just how it is! And you cant really fault people for saying something, they are just being nice and saying what they think, and I doubt that they have ill-intent. And they dont realize how many times you've already heard the same comment already that day.
Its more important to teach your child what is important to you and emphasize those qualities yourself, because you as mom have more weight in what your child hears than a whole bunch of random people's opinions.