I often tell participants not to be afraid of weights. Lifting a weight will not cause you to "bulk up", "have large muscles" or any of the number of concerns I often hear. In fact, strength training is crucial for increasing bone density; increase your energy level; increase your basal metabolism which causes you to burn more calories 24 hours a day. (You'll even burn more calories while you're sleeping.)
How do you know what is the right weight? If you are able to complete 15 repetitions easily, then the weight is probably too light. If you are unable to perform the exercise as it is designed, then the weight is too heavy and this may lead to injuries. You should feel challenged - if there are physical limitations (e.g injuries to the shoulder, wrist, etc.) then modifications to an exercise may be warranted and a lighter weight used. Ask questions on what is best suited for you-it is better to use proper form and feel challenged than to lift a weight that will cause injury. Don't feel intimidated to change weights during a set if you feel the one you have chosen might be a little too heavy or is causing discomfort and/or pain.
The correct weights will feel challenging by your last few repetitions, but won't force you to sacrifice form.