I'm way, way over 40 and started BJJ about two years ago. I'd really let myself go after retirement and "exercise programs" held no interest for me. Since starting BJJ I've lost close to 30 pounds and feel much better. I started back then after I called a couple of gyms and asked, "What do you have that's low impact that isn't Tai Chi?" (I tried Tai Chi but it wasn't for me - more like "martial arts dancing." Some people like it, though. I just couldn't remember all the steps.") The guy said "You want Brazilian Jiu Jitsu." I tried it and was hooked. I did have a few injuries at first - call them "over-enthusiasm:" rolling onto my badly placed hand, pulling a leg muscle during drills and so forth. Nothing kept me off the mat for long. I've seen no serious injuries at our gym and certainly no broken bones since I've been there. After I learned to warm up properly and keep my hands in I've had no more of those injuries and as you advance you kind of learn what's dangerous and you automatically avoid it.
FWIW, during classes I get most of the new guys now and I try to show them how to avoid actually hurting somebody with the bone-breaker holds. OTOH, after I learned to work smoothly rather than with muscle and gallons of sweat my weight loss slowed down so I had to attend more classes to make up for it.