Most of your body's weight should rest on your back foot in the classic billiards stance.
Many instruction books and websites say either "60/40 with 60% on your back foot in the stance" or "evenly balanced between both feet". I prefer to have more weight on my front foot during practice strokes and the final stroke.
Take an analogy from boxing and the martial arts. If you want to throw the hardest possible punch at a target ahead of you, if you rear backward you will lose all the momentum you'd like to send forward through your punching hand.
By contrast, you want your front foot forward in pool (left foot for a right-handed shooter, right foot for a left-handed player) to have weight on it so you can either 1) snap a break very hard or 2) keep any momentum generated during the stroke moving down into and through the cue ball.
The cue stick can never be level for most shots due to overhanging the rails with the stroke. Therefore the stick is angled down and needs to come straight forward also. That's "down and through, down and through." Setting your weight on your feet right makes for a simpler, purer pool stroke.
The correct weight distribution is a natural result of getting down precisely into the stance as shown step-by-step at:
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