If you haven’t heard it before, I’ll say it again: muscle responds to resistance or load. Whoever told you that loading the muscles with weights just gets you big, is a load of crap. Whether your goal is to increase bone density, get stronger, or sharpen the nervous system; the level of tension placed on the muscle dictates the measure of results. If you’re a woman doing bicep curls with those 2lbs insect weights, (you know those cute colorful dumbbells stacked neatly in the gym) it’s going to take you a long time to get lean. Or if your a man who’s been training for years and you’ve been trying to do the same amount of weight and reps since the invention of the dumbbell, more than likely you’re losing strength and muscle. 
People are often fooled by the fact that their muscles have gotten stronger since starting a work out program for the first few weeks. The truth is the first signs of strength gains are due to neurological adaptations, not muscle enhancement. It’s like learning to ride a bike. You haven’t gained muscles when you finally got the gist of it, but your nervous system learned to make the muscles work together to perform the task. After these initials signs of improvement, you have to challenge the muscles to get the quickest, most effective results.
The way to know how heavy the weight you should lift is based on your goals. What are you trying to achieve? Power? Strength? Leanness? Endurance? Once you figure that out, you can go on to deciding how many reps you should perform for a given exercise. For power, about 1-5 reps are optimal. To get stronger, 6-8 reps will get you there. To put on lean muscle, 9-12 reps will do it. For endurance, 13-20 reps are best. These numbers are just a guideline that has been tested on exercisers for a general rule. Once you know your goal, the amount of reps will tell you how heavy you should lift. If you choose 15 reps to target muscle endurance, the weight you choose should bring you to muscle fatigue at 15 reps, so much so that you can hardly get 16 without compromising your form. If you choose 10 reps for hypertrophy (muscle gain), you should be struggling by the time you get to 10, all the while keeping good posture. If you break these parameters by being able to lift way past your target rep range, the weight is too light.
Another factor to consider is your training age, which is the amount of years you’ve been training. If you’ve been training for yrs, your body will not respond to the same loads and reps imposed on it over time. You will actually get weaker that way. For instance, if I bench pressed 315lbs for 12 reps 1 year ago, I probably won’t be able to lift 315lbs for 12 reps today. Basically, as your training age goes up, your ability to do more repetitions decreases. What’s the solution? Lower the reps, and increase the weight! Ideally, if you’re a veteran in exercise, going for 6 reps at 70 percent of your maximum lift is best, as you get stronger throughout the years. This would maintain strength levels.
One more thing: If you think running will get you leaner faster, you’re mistaken. Your metabolism remains high for about an hour after running. However, your metabolism stays up for up to 24hrs after strength training! Running utilizes the largest muscle groups in the body, which are legs. The more muscles working, the more calories burned. You can get faster and more efficient results when strength training the legs, as they will optimally stimulate the hormones necessary to lose weight or tone. Although you can run to get the extra weight off, it’ll take you longer to get there than strength training. Does this mean your legs will look like two well defined tree trunks? No!! Remember the rep ranges and which one fits your goals. Does this mean that you should just train legs to lose weight? No!! A well-balanced program will incorporate the whole body, emphasizing the use of the legs in the exercise selection. In any case, choose the right weight to stress those muscles!!
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All the best and God Bless,
Ammo Athletics