Slight clarification to the original text reading of the power:

The large size of an object (car, house, whatever) is a function of the object itself and not fundamentally related to the ability Big. Technically, such demons don't have to have 'Big' (though, really, they should have the ability to reflect their physicality).

In short, Big allows the target to tolerate greater damage; that's it. The text about the target getting bigger is Color, and may not be 'required' in every instance. [1]

Big acts as a replacement for dice lost to physical penalties. It does not replace over the lost amount, just up to it. (If the lost amount is bigger than the Big, then the Big only replaces up to the demon's Power.) [2]

The replacement is in effect like padding, counting the whole conflict as one use of Big.

You still consider Big when estimating how hurt the character is per the chart for lasting damage on p 109 and 132. After that estimation is made however, Big turns 'off' and the character operates with the normal lasting penalties for everything until he heals.

Big can be used a lot like Vitality for purposes of checking the effects of lasting damage, even during the fight itself. [3]

Big, Armor and Vitality can all work simultaneously.