First of all, not too light. Throwing knives with a weight of around 200g are perfect to begin with. Lighter knives ("floaters") are hard to control and often bounce back from the target at random. For longer distances starting at 5m you can turn to heavier knives with around 250g or more. You will need quite some finger power and training to handle those, though.
Try it out: Take the throwing knife handle between your thumb and index finger, the blade points to the ground. Now make a jerk with your arm into some save direction. If the handle wobbles between your fingers, or the throwing knife even falls down, it is too heavy (perhaps some training can help).
Generally, heavy throwing knives are more stable in their flight. But by far not everybody has the strength needed to throw them accurately. I recommend starting with lighter throwing knives to develop the sensitiveness needed, a subsequent switch to heavier ones is real easy then.
For beginners, I recommend the Gran Lanxador by Nieto, it weighs about 200g and sticks in the target firmly.
The center of gravity (COG) should be in the middle of the throwing knife, plus or minus 1.5cm. Such a balanced knife will make nice, round circles in the flight. If the center of gravity is somewhere else, say the knife is handle heavy, the circles of the handle and the circles of the blade in flight will be of different diameter, making the trajectory less predictable.
Other people say that this is just an additional challenge, or no challenge at all, but I still prefer center-balanced throwing knives for two reasons: It is easy to change from one center-balanced knife to another, as they have the same turning characteristic. This is not the case with off-balanced knives, one would have to develop a new feel for every single knife. And secondly only center-balanced knives can be thrown from the handle and the blade.
To find the center of gravity, just lay your knife across your outstretched index finger and adjust till it is in balance.
There are throwing knives in the market with built-in adjustable weights. I do not recommend them, it is too easy to get obsessed with adjusting the weight. As explained above, you should prefer center-balanced knives. And if a knife does not stick, you change the distance or your grip, not the knife. Plus, the grooves for the weights are not easy to clean, and the weights are prone to come loose. One knife in our shop, the Nieto, has such an adjustable weight, but it throws best and perfectly if you just take it off.
For those who insist on throwing with knives whose center of gravity is not about in the middle, there is a golden rule widely accepted among knife throwers: Grip the light end! Hence, a handle-heavy throwing knife would only be held and thrown from the blade.