"show a leg" from the petty officers on Royal Naval ships demanding proof that the occupant of the hammock in port was not a skiving sailor but his 'wife'

Brass monkey story I heard was similar except that the balls fell off brass monkies due to the differential contraction between the admirals brass monkies and the iron cannon balls when the admiral went up north. The lesser captains had wooden monkies and these didn't contract and unseat the iron balls.

Square meal definitely comes from the square plates used on RN ships (but like stiff upper lip may well have been coined in the US).