Obesity & Pregnancy

I am almost 30 and overweight (considered obese according to the BMI charts). I have a couple of health issues (T1 Diabetes & high blood pressure - both very well controlled with meds/insulin). I have 1 child already (it took awhile for me to get pregnant the first time, but I was able to after taking a fertility drug). I’m wanting to try for another baby (and this will be the last one). My husband thinks I should lose some weight before trying again. I do agree that I need to lose weight, but my issue is: I don’t feel like I have time to lose a bunch of weight and then if we have the same issues with infertility and it taking months to get pregnant again. I was wanting to stop birth control and start trying now. The reason I’m asking for advice is this: is it possible to be obese and have a healthy pregnancy? My first pregnancy was pretty much smooth. I did have a c-section a week early due to high blood pressure, but overall, I had no issues and my T1 diabetes was controlled. Our first baby has 2 birth defects (nothing major but they were caught early on in a fetal scan). I sort of feel like my husband blames me for the defects (because of either my weight and/or my health issues) and I also think he is afraid our next will also birth defects, possibly worse. I’m looking for others to share their stories and/or advise about the situation- bonus points for those that have the same health issues as me. (Also, my plan was to have weight loss surgery after I’m done having kids) In my mind, I wanted to be done having kids by the time I’m 30 (I turn 29 in a few months)