How much does cement weigh after it has set?
Several things affect the final weight of concrete.

Concrete has many different densities based on its composition.  Standard "ready mix" concrete is often engineered for structural strength of 3000psi.  Since concrete is not this strong when it is first poured, a standard was created for when to test concrete.  This standard calls for the strength to be determined at 28 days old.  At this point, concrete has achieved about 99% of its strength, and will continue to very slowly strengthen over the next few years.  At 28 days old, I use a density of .085 pounds per cubic inch (146.9 pounds per cubic foot) when calculating structural load.

Concrete is porous.  In humid weather, concrete will absorb moisture from the air while in dry weather it will release moisture.  Even if you made the "perfect" weight today, it may decrease or increase over time.  This is why, when you buy concrete weights, they are encased in plastic.

Regarding your question on adding more or less water:  Contrary to popular belief, concrete doesn't "dry" to for it to cure.  Concrete hardens as a chemical reaction.  Adding more water than what is optimal to create the chemical reaction will only weaken the concrete without changing its final weight.  

As a side note, concrete cracks easily.  This is another reason why, when you buy concrete weights, they are encased in plastic.  With that not being a reasonable option here, and based on your application, I would strengthen the concrete mesh or fiber.  You can order "ready mix" with fiberglass fibers in it, or you can use a large hole mesh.  Too small of holes will create a fault line.  Aluminum works well because its density (.097) is close to concrete's density.  In any case, this type of weight is not to be dropped from any height.