First, a little correction: What does...(word)... mean? (Not 'means' - you have already added the -s for the third person on 'does', you don't need it also on 'mean') As Brandi said. So you could write this sentence like this: "But the trouble is that I'm inclined to be just a little bit choosy and particular - If you see what I mean." Teeny-weeny is used here to stress the smallness. But the excessive stress could be used to convey a sarcastic tone in some cases, depending on the context. Maybe she is trying to say that she is very choosy and particular, and she won't accept anything that she does not like.

Extremely small. Very very tiny. [emoji] It's a very childish word though.