A compression garment would help to reduce movement, although it will not stop it entirely, even if it is very tight-fitting. Sizing should be chosen to be as tight as possible without restricting circulation. You can wear these under a looser shirt if you are self-conscious about your body shape. As you lose weight, you should ideally adapt your sizing to match.
Something to consider is that the collagen and other connective tissues that are responsible for the elasticity of the skin exhibits a decline in function as one ages. In other words, as you grow older, you have less of it, and you what you have doesn't perform as well as it used to, which is why the skin of the elderly tends to sag and lack firmness. As you lose weight, depending on your age and extent of obesity, some of the skin's elasticity enables it to recover its former shape, but don't be surprised if, even after achieving your weight goal, your skin shows a considerable amount of sag or residual stretchiness. If you undertake vigorous activity without adequate support, you can cause additional stretching to occur, although the science on this is not entirely clear: I recall one study that suggested that women who wear supportive bras have less well-developed collagen in their breast tissue than those who have never worn a bra, suggesting that bras are a bit like a crutch, creating dependence over years of use. It is possible that short-term stress to collagen in a healthy, young adult population, can stimulate repair and additional production, improving skin elasticity through a remodeling process. But I'm not a dermatologist; for your comfort, I would advise using suitably sized compression garments throughout your fitness program regardless of weight or age.