Several things to unpack:
Does he say he's not eating or is it a neurotic family (dad's not eating!!!) member that may just need reassurance? Any objective signs of weight loss that you can use to sway your decision?
Treatment naïve? Has anything worked in the past? If so, up to how long ago was it that he on something? How elderly are we talking about?
BMI 30? Co-morbidities that you're worried about if he were to gain 10 lbs? Where I am, 30 is nothing. Going from a 30 to a 32 BMI isn't such a sin if he can look at you with a smile and say thank you doc. I'd take that all day long. It'll be hard/impossible to find anything for mood that does not have potential weight gain associated with it.
I don't think the issue is, should we be afraid to use a med that may cause weight gain, it's more, should we go out of our way to select a med that is even MORE likely than anything else to increase appetite and might cause weight gain in this overweight depressed individual, because of the report of appetite loss. Otherwise I completely agree with you.
I should have pointed out, that even if the med does improve the depression, which in itself I might expect to improve appetite even without a specific side effect of increasing appetite, that increasing appetite above and beyond that may not be such a great thing.
Absolutely treat the disorder and take the weight gain if you must. Just saying my goal wouldn't be to select a med specifically for increasing appetite in the overweight individual barring some other circumstances (weight loss as mentioned, risk for nutritional deficiency, sig distress from lack of appetite. Etc etc).
Also, I hate to point out, that there could be a lot of reasons you're getting the complaint (neurotic family was given as an example), but some people use food as a mental health coping mechanism in very unhealthy ways, like say binge eating pizza with family, and the depression getting in the way of that might be causing everyone involved to seek care, but it doesn't mean that they should try to get back to status quo.
A less humorous example would be someone who is a sex addict that is suffering ED, and it's causing them distress that they are not able to have sex. If you didn't know about the sex addiction, it would seem obvious that you should just treat the ED so the patient can get back to their sex life. That really makes the most sense if their pre-existing sex life was healthy. If it isn't, then just treating the ED might not be the right thing. They would need treatment for both conditions.
Sometimes patients want to go back to an unhealthy status quo. Change in mental health can prompt seeking care, but rather than just trying to restore a patient back to their "old ways," we should consider what life was like before and if tx and recovery from MH illness rahter than returning them to how they were, could forge a new healthier path forward.
Just my thoughts, some easier said than done.
Which is why this case is better approached with a thorough history and consideration of the whole patient, vs "oh you're not hungry here's a drug with a side effect of increased appetite enjoy your dinner"