"The less income someone has, the more taxes cut into basic living expenses (because a greater portion of that person's income is spent on basic needs)."

Covered by Milton Friedman's proposal of a flat tax with a minimum standard of living deductible, e.g. 10k USD. Furthermore, those making less than that 10k would get the 'refund' as some sort of social security. Developed in his book "Capitalism and Freedom".

"I'm not very good at describing this idea yet,"

What your describing is, as far as I can tell, the concept of "marginal utility".