have a thing for half-Asian girls

that he is attracted to half Asian women,more then likely sexually.
Half Asian refers to her being of split race.

Right. 'Having a thing' for something means having an interest in or attraction to that object.

it means half his thing is thinking of doing and the other half is doing the thinking

don't confuse him more

Excuse me?

Don't mind him. Just messing with you.

Actually, this is part of a dialog from How I Met Your Mother.

In Episode One of Season One, Barney Stinson says to Ted Mosley over the phone: "You remember, I always had a thing for half-Asian girls. Now I have a thing for Lebanese girls. Lebasense are the new half-Asian."

Barney's first dialog on the show - the one that made me fall in love with his character!