You won't get berated in this thread, many of us were starting with the same concerns.
You do need evidence, voy seem to be the most understanding, and most willing to prescribe at BMI 25. I don't know when you weigh yourself but most of us weigh first thing in the morning when we're the lightest, so if you're jumping on the scales later in the day as part of a consultation you might find you're a couple of pounds heavier anyway - I certainly did!
Sagginess is hard to say, it's very individual but I think less chance if you have less to lose, but there's only so much you can do re skin elasticity. However you might be able to change the way you feel about it with some strength training and gaining muscle in the longer term.
Side effects - again very individual. Personally I haven't really had any, occasionally a bit headachey and tired the day of the jab, or feeling a bit uncomfortably full, but nothing significant. I'm on wegovy, I was a bit worried that mounjaro would be 'too strong' for me.