This is complicated as it's not in the UK.
Posters need to understand there is a difference between a gift and a will.
Legally, the owner is you. It's a gift, not an inheritance.
Your father had an agreement to live there for life, and if this is in the contract (not his Will), then you should abide by that.
It would be a personal agreement between you to sell the house and provide him with another cheaper one.
Legally, he has no right to any surplus profit as he signed over his house and its value to you.
It's NOT an inheritance. It's yours now.
He needs to understand that you were given his house and it was not with the caveat that it could be sold and the excess profit returned to him.
If you decide to help him out with money from the sale, that's up to you, but legally, it's a grey area. It could be argued that although you are the owner, he had residence till his death. If he wants to move somewhere smaller, he may have grounds for using the outstanding equity to ensure he can live- but you need legal advice