in your sweats = wearing your "jogging trousers" or "pyjamas" = any clothes that you wear INSIDE and wouldn't dare wear outside as they look rough/terrible/cheap etc. So it means, "a guy who wants to show you off to the world when you are looking your worst" It means he is proud of you, even when you think you are not fit for it

Your sweats is the outfit that you usually wear in cooler temperatures for working out. Or when you are low on income to wear better clothes. Usually you don't have make up on as well. So when a guy wants to show you off to the world when you think you are at your worst, he sees you differently. He sees beauty instead and he is not ashamed to show you off. =) What a wonderful girl you are~

He wants to show YOU off to the world, not your sweats. If you just happened to be wearing sweats at the time, So what? He's happy to be with you. Proud to be with you. You are not your clothing.