If I make $100K it's entirely possible that my rent or mortgage is ten times that of a person making $10K, as well as my other costs of living.
If you doubt the veracity of that comparison, take a look back at property prices in the few years prior to 2008 and do the mortgage calculation yourself. It is not at all uncommon to find $5,000 p/month mortgages, and I know you can find rooms to rent for no more than $500 p/month.
So, if you buy the above intuition and want to use taxation to help maximize happiness...
What does happiness have to do with it? No-one in this country is guaranteed happiness. It's not the government's responsibility or right to make people happy, or even to try. Their charter ends at making sure people have the right to pursue happiness, that is all.