Under what circumstances? If you are still talking about rats in simple versus complex, stimulating environments, that is a far cry from the OP’s notion that his brain might get heavier when he learns some new fact, or lighter when he forgets something.
Natural environments are complex and stimulating. I do not know for sure, but my guess would be that what you are seeing in those sorts of experiments is that brains start to atrophy if they are understimulated for too long by being confined to an unnaturally simple environment.
I am confused by your confusion. Are you under the impression that synapses are all the same, or that they never change? Some will make stronger connections than others, because (for instance) they are capable of releasing neurotransmitter molecules at a greater rate.
With respect to increased synapse density, the recap of multiple studies I read listed examples from many different animals and specific tasks being learned in each study.
With respect to increased volume of gray and white matter, that includes humans and is relative to various specific tasks/abilities.
Since energy and mass are equivalent, it depends on if the energy your brain burned up while learning something has more mass than whatever physical/physiological additions, changes or rearrangements your brain has undergone to form the experience in gaining the new memory/knowledge.