Steve, the return is the dizziness/vertigo was likely the result of reducing Zoloft (sertraline) to below the therapeutic dose range of 50-200mg/day which, after the extra stress of your family moving away has seen a return of anxiety. If Zoloft was the cause than you should have experienced these symptoms even more strongly when you were at higher doses. Further evidence is that taking Xanax (alprazolam) eases them. Nor do I believe these are caused by a withdrawal effect. They would then have become apparent within days, not some 5 weeks later.
It can take 4-6 weeks for an increase in dose to become effective, so I'm not surprised that you haven't noticed any benefit after only 2.
As for the weight gain issue, yes antidepressants (AD) do cause this, with about a quarter of those taking them gaining weight. Zoloft is usually the least likely SSRI to do so. The only ADs with a better record in this regard are Wellbutrin (bupropion) and Effexor (venlafaxine). However, Wellbutrin is a very stimulating AD, too stimulating for most with anxiety. Reducing the antidepressant dose simply to lower weight is not a good idea, as you've discovered. There are better ways of keeping it in check. Probably the best is exercise. It not only does it burn calories, but it has been shown to significantly lessen anxiety and depression too.