After conventional or tumescent liposuction, the skin needs a period of time to heal and "reattach" to the deeper tissues. I have found that the skin is in pretty good shape at 4 weeks postop, but will gain even more strength by 6 - 8 weeks.
In our practice, we keep our patients in fitted pressure garments for 3 - 4 weeks or longer, depending on the skin tone of the patient prior to surgery. Once the 3 - 4 weeks have passed, we transition patients to more comfortable "Spanx" type garments (body support garments available at department stores) for another 4 weeks or so.
I feel that it is important to not exercise for at least 4 weeks or so after major liposuction as to not loosen the healing skin.