The only time I can think of the stone being used is in Dogs. In Dogs he is referring to the consequences of all the poor/evil decisions the person made throughout his life. And he's drowning because it's dragging him down.

And as for Pigs on the Wing, I think it's kind of a dislaimer saying "this is how things could be if nobody cared for each other". Because at the end he says "well you know that I care for you". So it's like he's saying "this is all true but there's still good in the world".

That's my interpretation anyway. I haven't listened to Pink Floyd in ages.