Technically speaking knees can't be weak - your knee, anatomically doesn't even exist, but is a joint where a number of bones, ligaments and muscles all join and interact.
People commonly feel that they have "weak knees" because the muscles that support the knee joint are undertrained. To compensate this lack of strength, they hyperextend the knee joint so the thigh is directly over the tibia, putting pressure directly on the soft tissue between the bones that acts as a buffer. This causes stress and pain on the soft tissue around the knee joint.
The best way to improve this is to fix the problem - a lack of strength in the muscles around knee joint and movements to reduce the stress on the soft tissue.
Any weight baring cardiovascular exercise - such as elliptical or cycling - will help, as will running, as long as you use a mid- to fore-foot stride. Heel strikes are biomechanically inefficiently and again put extra stress on the ankle and knee. These exercises will improve you ability to perform these motions.
However, it is probably also worth recommending looking into some traditional strength training as well. At the least, incorporating bodyweight squats will improve your legs ability to work through this range of motion. Start by doing repetitions starting from a standing positions with feet shoulder-wide apart and lowering until your thighs are parallel, then gradually work until you have the strength to lower your self until your rear touches your heels.
As always, your weight has a direct relation to the amount of pressure on your knees, so make sure you are eating a healthy diet and your height is as near to your ideal weight as possible. While BMI can be a flawed metric, working to fall within the "normal" range is a good place to start. Unless you quite tall or are actively weight-training, its unlikely that you are an outlier.