Bob is such a sponger. Sleeping at his brother’s, eating at his Mum’s and always borrowing from friends. Doesn’t he ever pay for anything?
To sponge off others is to get things free from people when you would be expected to pay for yourself or at least share costs.
It is a really graphic metaphor as the sponge absorbs water in that complete way mopping up all the moisture around it.
One of the drawbacks of being rich and famous is that there are always people trying to sponge off you. They think you are a gold mine.