From the statement we know the subject is about a stone, the property of the stone is that it is so heavy that even an all powerful being can not lift it. The paradox is that God should be able to do and make anything, but if He makes the stone, but then can not lift it, He is not all powerful. If he does not make such a stone, then He is not all powerful, so either option leads to the conclusion that God is not all powerful. How can this be paradox be resolved?
The issue here is the properties of the stone have a contradiction, this stone can not exist, the properties that define it are in contradiction, so the riddle is null and void as there is no such stone for God to make.
It would be the same as saying “Can God make a shape which is a triangle and a square in the same respect?”, there is no such shape as the definition of a triangle is incompatible with that of a square, its essence is different, and if we changed the essence, then the triangle wouldn’t be a triangle and the square wouldn’t be a square. These examples do not mean that God is weak, or unable to effect the outcome He wants, but that there is no outcome for Him to desire in this case, not because God is not powerful but because there is nothing to exercise His power over.
One could argue that God could change the essence of the stone, or the triangle and square, however that would not satisfy the question, as if the question stipulates a stone, with a known essence, it is not acceptable to change the essence of a stone in order to complete the challenge. So essentially these types of riddles exposes the concept of essences, or haecceity, whereby all things have definition and parameters.