How is weight training help me lose fat?

Add cardio. Strength training will not help you lose too much fat. Add cardiovascular exercise to your routine to make your strength training more effective and to add the fat burning benefit.
Burn calories. Weight training tends to burn more calories than cardio.
Boosts metabolism. Weight (or strength) training is very importnat to lose fat. A weight training workout boosts metabolism for the whole day and helps build lean muscle. Muscle is metabolically active - it needs fuel - and therefore helps you burn more calories all the time which helps with fat (as mentioned in faq 1).