It can vary I guess but about $2:00 per day is normal. The money goes to record your scores and forward them to the ATA. It also pays for operation costs as OH does not collect dues. It is the about the only money they get.
Ideally, the state organization can build up enough cash to help clubs with their trophy packages or chip in for dinners. But there really isn't much of a cash flow to work with and generally the state organization is broke.
The income and expenses of state associations it typically presented at each state meeting. These meetings are open to any member. I would think any state secretary would be pleased to mail a copy to anyone who requested it.