Basically, weight is used to calculate one thing. Whether or not your adventurer is overburdened with all the stuff he is carrying.
How much you can carry is determined by the following formulas:
Normal Load: Multiply the creature’s Strength score by 10. The result is the weight, in pounds, that the creature can carry around without penalty.
Heavy Load: Double the normal load number (that is, Strength × 20) to find a creature’s heavy load, the maximum weight it can lift off the ground. While a creature is carrying more than its normal load, it is slowed. Carrying such a load requires both hands.
Maximum Drag Load: Five times a creature’s normal load (that is, Strength × 50) is the most weight it can push or drag along the ground. The creature is slowed if it pushes or drags more weight than its normal load, and it can’t push or drag more than its heavy load over difficult terrain.
So basically, if you have too much stuff (but not more than your heavy load), your adventurer is slowed. This is a big problem. For most adventurers this isn't much of an issue, fairly early on in your career you should be able to pick up a Bag of Holding, and not have to worry about load except for the gear your wearing or actively using.
It's been pointed out in the comments that there are a couple of game mechanics that do use the weight of an item. Prestidigitation can lift up to a pound, Mage Hand can lift up to 20 (Psions and Wild Talent Masters have similar powers). So it comes into play occasionally on this stuff as well.