For what its worth...
Exercising during pregnancy REALLY helped my labor. There is already evidence of this, but I did my own personal case study lol...
I was sedentary for my other 3 pregnancies. My labors were all very long (shortest was 12 hours!) and painful...and recovery was fair.
This time around I ran until 31 weeks. When that became too difficult, I switched to cycling. I did that until 37 weeks when I finally had too much pelvic pain to continue.
I still gained a lot of weight, but under that fat I continued to keep my body in shape, if that makes sense.
My blood sugar was better this time around than with my first baby nearly 10 years ago, even though my weight gain was still excessive and nearly the same amount.
When I started having contractions, they were so not painful, I was still not seeing the need to go to the hospital when they were 2-3 mins apart because 1. I was only in labor about 2-3 hours at that point, so I knew I had longer because I have a history of long labors. And 2. because they weren't painful like my previous labors.
Hubby was the one that said we should go then. Regardless of pain. By the time we got to the hospital about 30 mins from then, my water started to leak and the contractions were stronger but I even said to the doc, I doubt I'm more than 4 -5cm because how long I usually labor. I was almost 8cm! With in an hour I was ready to push, and really only the last 15-20 were awful. But it wasn't worth getting the epi (which I had with my other labors) and baby was out in one push! (Though my others were out fast too)
I realize with each baby the labors go faster, but to go from 12 hours (baby #3) to about 4-5 hours total is pretty darn good.
Also I am 1 week postpartum and I already feel up to brisk walks. I have almost no pelvic pain, where as with my others I was slower to get back to feeling well.
So even with the weight gain, I can say that exercise really has a huge impact on delivery and recovery. I should say I didn't gain the weight with crap, I ate mostly clean, so I was good foods that I was over doing it with.