Some medical facts get twisted into very poor medical advice.
Obese women have pretty much the same amount of sex, as those of normal weight, and therefore have the same basic need for contraception.
The fact that weight loss can make some obese women more fertile doesn’t mean that you cannot conceive if you are obese.
If you are obese you have a large blood volume that distributes the levels of your medications, and that would include any hormonal contraception. Thus, your contraceptive pills might be a bit less effective, especially in the beginning. So you might need extra protection, such as back up condoms.
And have a frank discussion with your gyno about your ability to take medications consistently. If you are obese, skipped pills may make you a bit more likely to have an escape ovulation.
Hormonal methods of contraception can slightly increase your personal risk of having a deep vein clot. If you are obese you may also be at increased risk. So you may want to consider other methods, but it doesn’t mean you cannot take birth control pills.
Most contraceptive methods will not significantly change the weight of an individual. DMPA in some studies has been associated with more weight gain than other methods. But again, this doesn’t mean you cannot use an particular method if you are obese. Your gyno can help you navigate these competing concerns and successfully plan whether or not you want a child now.