Both have the same meaning to say something is weak. The only difference I would say, is that people tend to use the word Stupid when wanting to be more serious about being negative about something. Example: A.) Did you see that girl's hairstyle? It looked stupid. - The person sounds more serious and more judgmental. B.) Did you see that girl's hairstyle? It looked silly. - The person here sounds less mean and negative.

"Silly" can mean that something is funny, out of the ordinary or "stupid". eg; The clown at the birthday party is very silly. "Stupid" is a more harsh, rude word, implying either lack of brains, idiotic (intellectually or physically) or "without care" eg; It was a stupid idea to run across the road.