First off,DO NOT GIVE UP WEIGHT TRAINING. Cardio is an essential part of loosing those extra pounds but weight training gives you more bang for your buck. When you lift weights not only are you giving your body a cardio workout you are adding lean mass. Lean mass uses more energy than fat does. The more lean mass you have the more calories you are burning at rest.
I would also change your workout. Alternating between light and heavy days is good but it sounds like it isn't quite enough to get through that plateau. Look at changing variables such as volume,reps,number of sets,and tempo. I always try to change my routine as much as possible each month.
Sleeping late isn't that bad. I get up at noon everyday because I'm a server and my restaurant is only open at night. I've got blankets covering all my windows in my room so I can sleep without the sun bothering me.