I believe in theory, that if you pair an underpowered engine with an overweight vehicle, it will burn more fuel than the bigger engine in real world use, as you're going to be asking that little engine to give you 100% most of the time, versus asking the big engine for 100% not nearly as often.
That said, there are many other factors that may tip it one way or another, including driving style, and the relative overall efficiency of both engine designs. Theoretically, the small engine could be very efficient, and the big engine very inefficient, resulting in better fuel economy with the smaller engine.
So it's a general rule that an underpowered engine would burn more fuel in real world driving, but it won't always be the case.