The question is how to make the object heavier than the liquid
it displaces on the down side, than at the bottom change to lighter
than the liquid it displaces, than at the top change back to being
heavier than the liquid it displaces.

You cannot change the force of gravity, you can only redirect its resulting impact on objects...

Store kinetic energy created by gravitational force in springs e.g...
Create dampening material on rotors or created rotors on the same wheel out of different materials
The difference in kinetic energy release upon impact generates acceleration in the second case. (if talking wheels here)

It has been suggested that type 1 superconductors can be used to "lens" gravity.  Also, when spun, they develop a large gravitomagnetic moment in the vicinity of the rotating mass.

Greetings all,

@ AB HAMMER,
"if you can't beat it join it"   
Is that the same as a method to increase the effect of gravity?

@ overtaker,
"one weight raises and one weight falls"    ONCE

@  Brian334,
Sir do you know the difference in behavior of gases and liquids in terms of buoyancy effects?
Hint: viscosity
Sir please identify any object or material that does not have gravity passing through it unaffected?

@ Aquariuz,
Any redirect I have have found expends energy and is a net loss.
If you can explain a method that is not a net loss please share it with us.

@ zerotensor,
Very interesting thinking, but it seems that those methods are like building a nuclear reactor to power a flashlight.

@ pmotion,
Dams function because of a lowering of the level of the water passing through them. You may have one dam that uses 100% of the fall, or two that use 50%, but never two or more that use more than 100% combined.

Thanks for the serious replies,
Truth

Quote@ zerotensor,
Very interesting thinking, but it seems that those methods are like building a nuclear reactor to power a flashlight.

Hmm, a nuclear-powered flashlight...
http://www.google.com/patents?id=vcg0AAAAEBAJ