It's really dependent on the school though. Example, I got into WashU when I applied and would have had to take out over 40k/year in loans to pay for it even though my family's annual income was well below 100k. Some private schools do offer obscene amounts of aid, but there are also several top tier schools which do not.
As for the state school being more expensive, that's entirely dependent on what state you live in. I had friends that went to schools that charged less than 10k/year at the time, and that included room and board.
I'm not sure if the house necessarily matters, but assets is a good point. My parents had to included their stock and some other accounts in the FAFSA and it definitely hurt how much aid I was able to get. They were pretty appalled that the fact that they had lived conservatively and built up a solid retirement plan/savings to help send me to college ended up hurting us in terms of how much I could receive in loans.