Why is it it appears the larger the govt grows the gap between rich and poor increases?
Because you're an ignoramus.
You don't have a clue about any correlation between government 'size' and income distribution.
Let's see, wealth concentration last peaked just before the Great Depression - under 'small government', because the issue had to do more with the financial sector's behavior.
It was under FDR - with his much larger government 'size' - that the wealth concentration
went down for decades.
Oh look, there's Reagan's changes, like slashing the top tax rate, and the increasing of the concentration.
But wait, didn't it increase under Democrat Bill Clinton, too? Yes - Clinton didn't reverse the Reagan changes. He *did* increase taxes on the rich, not enough to stop this.
Oh look at that, George Bush greatly increasing government spending - and the concentration of wealth went up more.
The 'size of government' affecting income concentration has a little to do with something you don't mention - what the government policies and tax rates are.
Perhaps because when govt grows the people who benefit most are the rich?
When the government repealed Glass-Steagell, it didn't make the government 'grow'; yet it did shift wealth to top top from others as a net effect.
When the government taxes the rich more to expand medical care for all, it makes the government 'grow', but it reduces the concentration of wealth.