Wellbutrin is for depression, not anxiety, and as such can be stimulating. Drugs like Effexor are for both, but all can cause weight gain. You won't know until you try. The least problematic are probably Prozac, and then Lexapro, but even Lexapro has been known to cause significant weight gain and Prozac isn't usually that great for anxiety, but who knows? They're weird, these drugs, and affect everyone differently.
I was on Effexor XR for a few months, but I couldn't take getting sick whenever I forgot to take a dose. My doctor switched me to Pristiq, which works the same way as effexor.
I haven't had any problems with weight gain on either of the meds, though. I've actually lost a bit of weight since starting pristiq. I've been on it for months and my depression and anxiety have been put in their place!
Your eating habits may have changed a bit. You should consider what you've been eating and the amount. Consider whether your habits have changed recently or not.