"at a great cost"
A person who is thriftless is one who spends a great deal of money in a way that seems to be wasteful. The text says that the heir spends a lot of money to repair a house which has fallen into decay when the heir could have spent much less if he had just kept up with it. This idea is continued when it says that a house which one built at a vast expense is then ruined and another is built at "no less charge."