I repair aluminum frames all the time. Most commercially available 7005 chain stays are pretty thin and you can see a couple of fairly cold welds on that frame as well. With all due respect to other opinions, repaired frames seem to hold up quite well without a secondary age cycle.

If both the chain stays are cracked in the same place, they are too thin and should be replaced.

Most of what was said regarding "finite fatigue life" is true. I don't suggest you repair this frame. Mostly due to your size. Aluminum frames are made to be light and last long enough. Not forever.