> the bottom 50% accounted for a measly 3% of all tax.

Of course they do, that is a symptom of the problem. Take an absolute extreme of society: one person has all the wealth, and everyone else has nothing. Obviously, that one person will pay 100% of the taxes, and everyone else will pay 0%.

Today, we see a similar but less extreme situation. It's not intuitive at first glance, but think about it for a few seconds and it makes sense: if you want a more balanced distribution of tax burden across society, you need a more balanced distribution of wealth across society.

Accordingly, if you want the bottom 50% to pay more, you actually have to tax the rich more to reach a more equal distribution of wealth.