Pilates can be brilliant for a weak pelvic floor. But you may need to go easy on other abdominal exercises, including the 'good' deep abdominals, as too much exertion here can 'push' things out and down if your pelvic floor isn't strong enough to contain things. You may also find that your pelvis isn't as stable as it otherwise would be, especially if you have actual pelvic floor damage, and you may need to go easy on exercises that involve movement in the pelvis (e.g. knee drops, even knee floats). If you have real weakness to the extent that it is e.g. contributing to incontinence, gynae/women's health physio is a good idea.
As for pilates and hypermobility, it's so tempting to enjoy the wide range of movement that you naturally have, taking wide leg positions, exaggerated turn out, etc. What you really need to do is keep those movements very small and concentrated, trying to bring everything to the centre and strengthen the core as much as possible.
A good and experienced instructor should know all of this.
NB: Am not a pilates instructor, but have been doing it for over 10 years and have both hypermobility and serious pelvic floor damage.