The usual objection to raising taxes on the wealthy or corporations is that such taxes undermine economic growth; yet there is remarkably little evidence to back up those claims. Studies instead have emphasized that neither business tax cuts  nor estate tax cuts  play any significant role in local economic growth.
Instead, the sad truth is that almost every state tax system requires working families to pay a higher percentage of their income in taxes than their wealthier citizens. In fact, as the Institute on Taxation & Economic Policy detailed in their 2003 study, Who Pays?:  "[O]nly four states require their best-off citizens to pay as much of their incomes in taxes as middle-income families have to pay." As the graph below from ITEP shows, the average family pays significantly more of their income in state taxes than the wealthy.
A report  by the Center on Budget and Policy Priorities and EPI emphasizes that making state tax systems more progressive is also a way to mitigate the broader trend of growing before-tax economic inequality.
Core Policies to Make Tax Systems More Progressive include:
General Resources to Make Tax System More Progressive
- Institute on Taxation and Economic Policy (ITEP) - Guide to Fair State and Local Taxes 
- ITEP - Who Pays? A Distributional Analysis of the Tax Systems in All 50 States 
- Progressive States Network, Raising Revenue Through Fair Taxes 
- Progressive States Network - Dos and Don'ts of Coping With State Budget Crises 
- Economic Policy Institute - Rethinking Growth Strategies 
- Center on Budget and Policy Priorities and EPI - Pulling Apart: A State-by-State Analysis of Income Trends