Hi Jane, there is overlap between anxiety and depression, and some of the meds can treat the symptoms of both. Tell your doc that you are concerned about weight gain- again, some meds are better than others in that regard. The older tricyclic anti-depressants tended to cause weight gain, but the SSRI's (zoloft, prozac, wellbutrin, lexapro, effexor, etc) which are used for anxiety and depression now as the first line treatment- not so much. In some people they even cause a slight loss. Slight being the operative word.
It can take a couple of tries to find the right SSRI. I've done really well on them, but not all of them. The chemistry is slightly different with each one, and your own body chemistry will dictate which you respond to. Try to be patient, and if the first one doesn't solve the problem, remember that it doesn't mean meds won't help.
My bias will show here, but the research has shown that for anxiety AND depression, the MOST effective treatment is meds plus therapy. That's because there are habitual ways of thinking (or worrying) that an effective CBT (cognitive) or DBT (dialectical behavior) therapist can help you to recognize and combat.
Or, as our grandmothers would have put it, how to recognize the things we can change, accept the things we can't, and be wise enough to know the difference.
There are many kinds of good therapists. If a trusted friend recommends one who doesn't describe themselves as "CBT" or "DBT", just remember, the most important quality in any therapist (assuming basic competency as a given) is fit. If you like them, and feel heard and understood, chances are, therapy will help.
Could be both. My depression led me to have anxiety attacks. It stinks to have both. Good luck with you at the doctor. I am not sure about medications and weight. I am slightly overweight but none of the meds I have taken in the past or present have changed that any.