Weights !!!

Eating in a caloric deficit is the most efficient way to lose weight. The difference in calorie burn between lifting lighter weights with more reps or heavier weights with fewer reps is, generally, negligible, assuming you are using proportional weight. By that I mean using appropriate TM %s and reps. If your 4RM is 50 kg, for instance, a reasonable 10 rep weight would be 40 kg or so. 5 kg would be extremely low. I don't want to say that it would be a waste of your time to do 10 reps at 5 kg but I don't think it would be especially useful.

Weight loss is a culmination of many things.

Plenty of sleep
Healthy eating
Caloric Deficit
Regular Exercise Plan
And many more factors

By using MFP you can manage and count your calories to promote a calorie deficit which will in turn result in weight loss.

I think both methods (light weights or heavy weights) will burn calories and increase your strength. I would also recommend cardio if applicable at least 2 times a week.

Light weights will strengthen endurance
Heavier weights can increase power

So try an incorporate both types through your week for weight loss. Remember to warm up before each workout to prevent injury.

I prefer hypertrophic rep ranges on a cut. Will usually do a few 4-6 rep ranges of whatever compound lift on the body part I'm working and then Hypertrophy ranges for the follow up lifts.

No reason other than preference though.