I think a study once showed that 1 in 400 BASE jumps by folks with skydiving certs end in death. Make sure you get a lot of skydiving experience in first and then maybe do bridge day. Even then, people die at bridge day every year. BASE jumping doesn't allow time to throw a reserve so you'd better have your main packed correctly. A 1 in 400 chance of dying may be worth bariatric surgery and being thin for the rest of your life. I'm not sure it's worth a 60 second experience.

I'd like to think hang gliding offers nearly the same rush as BASE jumping. Gliders are a little more complicated to operate than a parachute, but they allow you to do aerobatics. Flights also last longer- twenty or thirty minutes in ridge lift and hours in thermally conditions, or five minutes for a sled run. You can also do it legally just 90 minutes from NYC. A study done ten years ago suggests that the risk of death or serious injury for registered pilots is closer to 1 in thousands per year for active pilots. Many of those injuries happen when landing or flying in dangerous conditions that you can learn to avoid. Hang glider pilots under 40 effectively double their risk of accidental death for ~20 flights per year, which constitutes a more acceptable risk/reward, IMHO.

Make sure you line up primary or supplemental disability insurance before you start training for any extreme sports. The insurance companies all ask beforehand and insert a rider if you are already participating. This includes motorsports racing, skydiving, hang gliding, paragliding, Tech SCUBA diving (below 130 feet or caving), ballooning, rock climbing, and bungee jumping.