If the pot can contain twice as many in volume, is it twice as heavy? Suppose that I have two pots that look like similar cylinders (e.g. Mason jars). I know that one of them can contain twice as many in volume than the other. If both are empty, is the bigger one twice as heavy as the other?
Intuitively I would say that it is less than twice as heavy, but I am not sure. Mathematically, I do a cross multiplication and conclude that the bigger one is twice as heavy, but it seems wrong to me. How to solve this problem?
Note: This is for an actual real life problem. I filled up the bigger pot and sealed it but I forgot to weigh it before and now I want to know how many grams of food it contains.
EDIT: The width of the walls seem to be the same. Can we find what is the weigh of the bigger one given the weigh of the smaller one?

If the pots are made of the same thickness of metal, then no.
Let $r$ be the radius, and $h$ be the height.
Let's say the pots have the same shape, so $r/h = C,$ some constant.
The weight of the pot is then proportional to the outer surface area:
$$ A = \pi r^2 + (2 \pi r^2 / C) = \pi r^2\left(1 + \frac{2}{C}\right).$$
But the volume is
$$V = \frac{\pi r^3}{C}.$$
Therefore, a pot that holds double the volume has an $r$ that is $\sqrt[3]{2}$ times that of the smaller.  But the weight, then, is $\sqrt[3]{4}$ times that of the smaller one, not double.
Of course, all bets are off if anything is different about the thickness of the pot, the form factor, etc., so it's better just to weigh then both.
