I am just starting off and have made a 3 days per week routine with body weight and dumbbell exercises. I am not seeing much of a progress in terms of fat loss two weeks into the routine.(I do 16-20 sets) It might be too early to decide, but I am thinking of doing some light exercise on the rest days also to burn some calories. Can I do cardio etc taking care not to use the muscles that recover the from previous days workout, to lose fat faster?
Usually this would be called an active rest day, and is something that I find very effective. I lift 6 days a week then do cardio whether it be riding my bike, jogging, running, or soccer drills. I find it quite helpful. It gives your muscles time to recover but you are still getting your daily dose of exercise. As you said, it is important to avoid using the muscles you just trained. This is why I often do my leg day first day of the week or mid week, so my cardio day is not back to back.
Days off from lifting, known as "rest days", are designed to let your body heal from the damage you do during training. Oddly enough, the more progress you make in strength training the less frequently you can train at maximum because you get very good at damaging your body.
Putting it another way, the cumulative exercise (a.k.a. damage) a trained athlete can do to their body is much higher than a novice. As such, a new weight lifter can perform at maximum nearly every day, with no rest days, because they simply don't need that much time to recover. EXRX has some good definitions:
Expected level of strength in a healthy individual who has not trained on the exercise before but can performit correctly. This represents the minimum level of strength required to maintain a reasonable quality of life in a sedentary individual.
A person training regularly for a period of 3-9 months. This strength level supports the demands of vigorous recreational activities.
A person who has engaged in regular training for up to two years. The intermediate level indicates some degree of specialization in the exercises and a high level of performance at the recreational level.
An individual with multi-year training experience with definite goals in the higher levels of competitive athletics.
Refers specifically to athletes competing in strength sports. Less than 1% of the weight training population will attain this level.
Being honest with the category you're in is important: training programs are optimized for certain categories. Those programs seek to maximize the benefits of the category and minimize risk. Related to Untrained, here's another excerpt from EXRX:
Untrained participants (less than 1 year of consistent training) experience maximal strength gains with an average training intensity of 60% of their 1 RM or approximately a 12 RM, training each muscle group 3 days per week. Novices weight training 2 times per week may make approximately 80% of the strength gains as compared to training 3 times per week.
That means you should be doing a full body routine, three days a week, hanging out in the 12 rep range. Each time you workout you should be hitting all major muscle groups, focusing on compound lifts. You should notice strength increases weekly, sometimes more frequently; in other words you should be regularly and gradually increasing your weights. Starting Strength by Mark Rippetoe is a program you'll see referenced a lot for good reason.
So on your rest days, which is every other day, you can do whatever you like but make sure you're not adding a lot of physical stress. Yoga, light cardio, sports, and things of that nature are good. You definitely don't want to be sedentary (at all, ever), but don't steal the recovery time that your body needs.
That type of discipline gets more important the stronger you get. A lot of people are on perpetual plateaus because they don't have a proper program that maximizes work effort and rest.