Here's my guess, for what it's worth. "Roof" and "slater" go together, so that's OK.
Many years ago, poor people would go to the local shop for food, etc. but they often could not afford to pay until payday came around, so what they owed the shopkeeper was "put on the slate". That was a piece of slate (!) on which customers' debts were written, so if you bought something "on the slate" you bought something on credit. Does this fit?