The larger the objective, the more light it will gather. However, the amount of light you eye can ever actually use is limited to how large the pupil in your eye gets in low light. This is around 7mm MAX for the human eye. So the exit pupil diameter (the size of the spot on the ocular lense where the light comes out) needs to be 7mm for you to get as much light as your eye can use.

Exit pupil diameter is determined by dividing the maximum usable diameter of the unobscured portion of the scope' s objective lens by the actual magnification of the scope. (Same for a pair of binoculars!) For example, an 8-power scope needs to have a 56mm objective lens to give you a 7mm exit pupil size. A 4X needs a 28mm objective, etc., etc.

Any scope which has an objective diameter that, divided by the max power setting, gives an exit pupil EXCEEDING 7mm has an objective lense that is TOO LARGE, and the excess exit pupil light is just wasted. This means, for example, if you had a 4 power scope with a 40mm objective lens, the exit pupil would be 10mm, or 3mm MORE than a human eye can use, so you' d be dragging the extra scope size and weight around for no benefit!