To lose weight with weight training you want to structure your workouts with two principles. Firstly you need to make sure you are using muscular endurance training. Secondly you want to structure your workout as a HIIT session.
What is muscular endurance training? This is the type of muscular training that creates muscular definition, but not size. It is the kind of training that focuses on the muscles ability to perform repetitive movements for long periods of time. To achieve this you want to make sure the weights you use are making you reach failure, when you cannot continue the movement, at around 12 to 16 repetitions.
What is a HIIT session? HIIT (High Intensity Interval Training) is when you perform periods of hard training that are separated by periods of rest. An example using weight training is by doing a circuit. You would preform 4 or more exercises straight after each other, and then rest for 1 or more minutes. How many exercises you do and how long you rest for depends on your fitness level. Individuals who are new to exercise may want to have a rest between each set of an exercise. Over time you would build up to doing full circuits.