I'd rather not switch to private messaging. This is a thread that is still open and all PF users must have the chance to read it, offer their comments and profit from it.
There are two total forces acting on the contraption because there are two agents that interact with it, each in its own way. The Earth and the surrounding water. Here is the breakdown of the constituents of these forces. This applies to both figures A, B and C.
Earth
To get the total force exerted on the contraption by the Earth, you must add
(a) the weight of all the water contained in all parts of the contraption
(b) the weight of the skin of all the bags that form the boundary with the surrounding water
(c) the weight of the tubes, tank, platforms, etc. that form the rigid structure.
These are the weights measured in air and are the sum total of all downward force, i.e. the total downward force in all figures A, B and C. This is the force with which the Earth attracts the contraption and is the same
regardless of whether the contraption is in water or not.
Fluid.
The total upward force is the buoyant force and is equal to the weight of the displaced water. As we discussed earlier, the contraption will float or sink depending on how the
variable weight of the displaced water compares with the
fixed weight of the contraption. I hope this answers your question.
I started writing this before
@A.T. posted, but I will leave it as is anyway because it is more detailed.