The general advice for EDS is to avoid elective surgery. Another advice is to keep your weight down and be as fit as possible. With WLS it's a contradiction of the two.
Just to clarify I was diagnosed with hypermobile type EDS after I had a gastric band.
From what I can make out any type of EDS and any type of implant is a problem waiting to happen. Now some may work fine, skin elasticity from classical type is also often there as an aspect of hypermobile and vascular types (for vascular EDS it's HIGHLY unlikely that weight loss is an issue). There are ways of checking - pull the skin on an extended elbow, also your neck and back of your hand. If you can pull it further than most people can then it's a sign of classical crossover. This can affect healing and how the body reacts to alien objects such as a band (but seemingly not stapling). Why this jump in logic? The skin is an organ - it often gets taken for granted but it's indicative of how other organs in your body may be different. Increased elasticity in the skin may (this is a theory that hasn't been properly researched, I can't find a paper on it but I'm aware of discussion in the medical community) I repeat **MAY** influence the elasticity of some internal organs. I'm sure there's a PhD candidate out there who could take this topic further, but it's all theory at the moment.
My own personal non-professional opinion is that the only WLS a bariatric EDS candidate should consider is RNY or MGB (possibly sleeve). Certainly not the gastric band due to increased risk of band migration. With the sleeve as it's purely restrictive and there's an unproven theory that EDS pouches are more likely to stretch, the long term benefits may be less. However with RNY there are increased risks of malnutrition and EDS patients often have absorption issues of vitamins before bariatric surgery so levels need to be very carefully monitored. MGB is a compromise but with the larger sleeve style stomach may have shorter term losses but with some of the malabsorption aspects it's questionable if there's a significant difference in risks to RNY, although generally it's considered a little bit safer. Ultimately the difference between RNY and MGB is largely down to preference and surgeon recommendation. While cost can be a factor, it's good to discuss the issue with your surgical team and consider their recommendations.