I can't give any insight to the weight issue, but autoimmune has been known to me since my early teens.
I have scleroderma, rheumatoid arthritis, positive ANA for years and positive Rh factor (and PCOS & Endometriosis). When I was first having autoimmune problems I had to do blood work every other week for 16 weeks to see what the heck was going on. I was also dx with leukopenia (low WBC in the blood). Since then, I've had so many autoimmune problems and yes, I associate PCOS (in my case) to autoimmune. If the autoimmune panel comes back w/ a positive ANA or any other "indicator" seek help from a rheumatologist.
Sounds like you are on the right track w/ your weight - did they tell you how much to lose to do the lap? I have read that it is more difficult in overweight women, but I know very little about it. You may want to contact the Endometriosis Association w/ questions regarding weight & lap. They are very helpful. I've found I have to follow a strict diet to control my weight and pain (certain hormones in milk, meat, and sugar bother me).
Speaking of being tired, have you been tested to see if your hormones are alright? Do you perhaps have a B12 deficiency? See if the dr can run a panel to check all the levels of hormones, etc that your thyroid produces.
Theres a book pusblished by the Endometriosis Association that I have found really helpful (their 2nd edition of Endometriosis - available at any bookstore). If you contact them I think they can send you all the Endo information brochures for free too.
Although it sounds like your dr's are working with you, just be sure to know you are your #1 advocate. If you are in pain, don't give up getting answers.
If you have any questions, let me know. Otherwise I think you are on the right track to getting some answers!
