It's no myth. Some returnees and their doctors agree they did get shorter – if at least temporarily. The 60 to 90 pounds of gear around their torsos, shoulders and heads likely caused their spinal discs to compress, making the soldiers shorter and causing back pain.
Is there a height limit to be a paratrooper?
Strictly speaking, there is a max height for parachuting based on harness, canopy and a couple of other things. If you're not over about 6'6" you should be OK.
How much weight do paratroopers carry?
A Weight on Their Shoulders
Paratroopers carried an average of 70 pounds of equipment. Officers averaged 90 pounds of gear. With the parachute, men weighed in at 90 to 120 pounds over their body weight.