Very interesting ideas. I don't know if you're wrong or not - but as I enjoy playing devil's advocate - i will probe at what i perceive as the weak spots in what you're saying... just for fun though since i really don't know if our premises are correct. So i am speculating along with you.
But first i would like to mention that we know (by measurement) that the diameter of the Earth is increasing at the equator - like many people, the Earth has a bulge around the middle which is getting larger. You can investigate why this is but it will boil down to conflicting gravitational pulls (Earth/Moon and mostly the Sun).
But this is different that the claim the Earth is expanding like a balloon being blown up as the Earth expansionists seem to be implying.
Anyway back to the infamous E=mc2. Nothing like bringing some Einstein into it
All equivalent:
E=mc2
m=E/c2
c2=E/m
And there is little doubt that the Sun is bombarding the Earth with visible and other forms of light/energy. So I think what the Earth expansionists are wondering is where does all this energy go? Much of it is of course reflected off the Earth's surface and back into space - but that would still leave a great deal of energy being received by the Earth, right?
Well i would say our moderate climate is the answer to where the majority of the energy goes. The energy is not lost but remains in the form of heat. Heating of the interior of the Earth which keeps are oceans relatively warm which keeps our climate hospitable (with the aid of our atmosphere which keeps just enough of the good energy in).
Luckily we have a few other planets to look at to see what is happening on other worlds. None seem to be expanding and they are also being bombarded by the Sun's energy. Little Mercury and mysterious Venus are even closer to the Sun and they do not seem to be getting larger. Nor does Mars - which is further away.
And if you think the Earth would expand because of energy - then for sure the gas giant planets like Jupiter and Saturn would be even more prone to expansion since gas takes very little energy to begin expanding (which is why they are so large in the first place) and yet they do not seem to be expanding either.
I'm sure if you did some digging around you could find out how much energy the Earth absorbs from Sun annually - at least a ballpark figure anyway.
anyway - just some off-the-cuff ideas that i think are related to what you're saying.