Circuit training?

This is the best way to burn fat regarding weight lifting. It's easy, but it can be difficult. Personally, I find it to be more difficult than a lot of cardio sessions including HIIT.

Say you have 8 different exercises for the day, 3 sets for each exercise. What you'll do is 1 set of your first exercise, rest for 15-20 seconds to get a gulp of water, then do the 1st set of your second exercise, rest again, and then continue the process until you do 1 set of each exercise. Then you'll rest for 2-3 minutes, and do it all over again. You do this process for a total of 3 sets, so each exercise is done 3 times.

The pros: burns more fat, same amount of lifting in less time, gets your heart working.
The cons: probably won't pack on as much muscle, not as fun.

Try it out.