Close to goal weight, OK to start exercise now?

I’m in the last 10 pounds of goal weight. I’m 5’6″ and 133, want to get to 125. I’m 48.

I exercised for years, mostly weight lifting with some cardio. I was side-lined by a back injury a few years ago and only now feel excited to start up again. However, I always put on weight with weight lifting and don’t want to feel discouraged as I’m getting closer to goal weight. Also, my protocol isn’t perfect and I haven’t stayed on it perfectly for more than 7 days straight, I usually eat off plan a bit. Should I wait to start working out until I found correct protocol and reached goal? Are there certain exercises I can do now that won’t add weight, besides walking which I dislike? thank you