The typical weight of a 6lb gun is 16-17 cwt (with longer patterns seen on e.g. the quarterdeck of early 1st rates being heavier (up to around 20cwt)).
Ammunition weight is 8lb per shot, powder plus ball.

The typical weight of a 12lb naval gun is 29cwt (with longer patterns up to 34cwt). Ammunition weight is 16lb per shot.

On the other hand, moving to 12lb carronades goes to a 6-6.75cwt ordnance weight (with a carriage which is a higher proportion of the lighter weight. Ammunition weight is 13lb per shot. Remodelling of the lower port cill to mount the fighting bolts is necessary, but the side framing and top cill can be left undisturbed.

(The later fit of guns is an increased burden - there are more guns (14 carronades, plus a pair of guns, compared to 12 pieces), and the weight is higher. 18lb carronades are around 10cwt, and ammunition 19.5lb per shot. 9lb guns 26cwt (in short patterns) and 12lb per shot.

(I am using RN weights as I have data for them which I haven't been able to find in a consistent manner for US equiivalents (but typically when I have both RN and USN weapons there are only small differences for 'similar' weapons).

When you have a change to larger guns it is typical to see a reduction in number (see Lynx, with half the number of 12lb *guns*, compared to similar 6lb vessels, despite being pierced for a larger number consistent with the smaller ordnance or alternative carronade fits which show the 'full' fit of guns.

Note the total loading of the vessel is higher because of the ammunition than the simple comparison of gun weights alone - and the 'remodelled' version was not rated very highly - as quoted above it was slow, crank and cramped, while the earlier 1802/3 rearmament was considered a better suited configuration.