I suppose the theory that extra weight is to be avoided comes from various fuel saving tips that are about and it's true that it is often recommended that you minimise the extra weight you carry around.
Well - yes - but only as part, and a small part at that, of a programme of measures such as keeping your speed down, avoiding harsh acceleration and braking and so on.
As Culzean points out, temperatures have dipped quite a bit of late and I've found my mpg always dips a bit when this happens.