I think that most SSRI's require a work up to/work down from dosing to maximize results and also take several weeks to even really start working so obviously just taking it for one week of the month isn't going to be effective.
As far as the weight gain goes, I think there is a couple of different issues. One is people "expect" to gain weight because someone told them they would (or they read it somewhere), so they do. Another is some folks don't eat well/enough when they are depressed/anxious. Once they are feeling better, they eat more and gain weight. Or if the SSRI makes you feel fatigued, you might be less active and gain weight. None of these are really so much a "side-effect," but rather sort of a consequence for a changed behavior after starting a different medication.
I guess I'd rather lose 10 lbs myself than have irrational thoughts each month, but if the weight is a real issue for you, I work on resolving ways to deal with that while still taking the medications even before you start so you don't sabotage yourself after you start taking the meds.
Good luck!