Why did ships carry mixed gun calibers?

Was the lack of uniform armament mainly caused by weight distribution?

Yes. Heavy guns had to stay low, with lighter calibers on successively higher decks because of construction and stability limits.

Uniform armament sounds simpler, but it would place too much weight high in a wooden sailing warship. Designers therefore concentrated the heaviest cannon on the lower gun deck and stepped down to lighter weapons above. The mixed battery solved structural and stability constraints. A ship's gun plan must be read together with hull strength and vertical weight distribution rather than as a standalone measure of firepower.