Sometimes. Wellbutrin does not generally cause weight gain (and is often used specifically because it doesn't), although rarely it might cause weight gain. Prozac is somewhat more likely than wellbutrin to cause weight gain, but again generally does not. Cymbalta (duloxetine) is probably about as likely as Prozac to cause weight gain, but again generally does not cause significant weight gain.
No. Wellbutrin doesn't Prozac may but also can have weight loss Cymbalta (duloxetine) may in my experience few pts complain of wt gain with any of these meds.