Pots actually weigh less then barrells not more. Here is the entire wiki article, with the paragraph highlighted pertaining to weight. I start making tons of wooden pots right away. I dont really mess with making barrels since pots do hold more. Also, the note about stack of alcohol vs food is listed in this snippet as well. 60 total prepared meals, or one STACK of booze. Not sure what the maximum booze stack is, but I imagine if your brewer manages to make a booze stack sized @ 60 then it will go in a pot, but I dont remember how the booze stacking works. Basically though, your dwarves can stick tons of different stacks of meals into a single pot, totalling 60, but with booze since its liquid it can only store one stack. So regardless of stack size only one type of booze can be in a pot. If you stuck antoher in there they would just be mixing together is the logic here.
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Pots are containers that function much like barrels, but can be made from other materials. They can be made from stone by a stone crafter at a craftsdwarf's workshop, ceramic at a kiln, glass at a glass furnace, wood at a craftsdwarf's workshop, or metal at a metalsmith's forge. Pots made from stone, stoneware, glass, wood, porcelain, metal, or glazed earthenware are water-tight and can be used to store liquids, and even for brewing. Unglazed earthenware can only be used for storing dry items. Metal pots are made using the metalcrafting skill, as opposed to metal barrels, which use the blacksmithing skill. The game refers to these containers sometimes as "pot" and sometimes as "large pot" but there is no actual distinction. Pots are stored in the Large Pots/Food Storage section of the Furniture stockpile. Pots are visible on the haul-for-trade screen under Tools section. Workshops that require a barrel for construction cannot use a pot instead.
Large pots are currently 1/4 as heavy[1] as barrels made from the same material, and they have double the capacity. Typical wood is density 500, while typical stone is 2670 - so a stone pot will typically weigh 33% more than a wood barrel, while carrying twice as much. Only lignite or jet stone pots will be lighter than a typical wooden barrel. Fire clay 'stoneware' pots weigh the same as a wooden barrel, while earthenware pots are lighter but may need to be glazed.
Metal pots are strictly superior to metal barrels, gaining the weight savings and requiring only one bar to construct instead of three, with the only disadvantage being the special cases where pots cannot be used. Similarly, wooden pots are strictly superior to wooden barrels for hauling and storage.
A pot can accommodate up to 60 prepared meals, but, like barrels, will still hold a maximum of one stack of booze, regardless of size.
Stone or metal large pots can also be used to conserve wood, if needed. They also allow trading valuable prepared meals to the elves, in the event you don't feel like exporting magma instead require cloth or find a useful exotic animal for sale.