Is this like "I, like you, want to be thin" or "I, in addition to other things I want, want to be thin?" Or can it mean both?
The first one, rather. For the second version, I'd put "też" before "szczupła".
I think it's more "chudy" http://dictionary.cambridge.org/dictionary/english-polish/skinny
szczupły is healthy thin, only about a person.
chudy is thin about many things, and skinny about things like food (with less fat). It's less positive than szczupły about a person.
The best translation for "szczupły" would be "slim" or "slender". Calling a person szczupły/slim/slender is a compliment. Calling someone chudy/thin/skinny is not.