This is related to How did the Basilisk survive for a thousand years? The basilisk in "Chamber of Secrets" is shown to eat small mammals and reptiles, from the skeletons that are discovered. I understand that snakes that don't get enough food stay small, and one way to get a bigger snake is to feed it more. The basilisk must start small, as it hatches from a cockerel's egg.
If it was eating stray familiars, in quantities required to grow as big as it did, why didn't anyone notice? At the very least, wouldn't older students mention that animals had a tendency to vanish so either bring a cage or don't get too attached? (How did Neville's toad, Trevor, keep coming back?)
I understand that real snakes actually digest the bones of animals too, so perhaps the digestion of a basilisk is different enough that it spits out/excretes the skeletons? Would this be enough of a difference to explain how it uses less of the available food source but grows bigger?
Additional thought - is there any evidence that the basilisk ate bigger mammals, eg students?