The maximum carry weight is the amount a soldier can carry without getting TU penalties. It's calculated by
8kg + 0.3kg * strength. This value and others are described (and can be changed) in
For example, a soldier with strength 50 would have a maximum carry capacity of
8kg + 0.3kg * 50 = 23kg. Since 80% of 23kg is 18.4kg, said soldier will not gain strength if they carry 18kg or less, but will gain a progress point towards strength for each tile they move carrying 19kg or more. This means that strength increases every mission as long as each soldier moves at least 20 tiles with appropriate weight.
I would recommend filling each soldier's carrying capacity to the brim whenever you check their equipment. That way they'll still continue to gain strength even when you have multiple missions without updating the equipment between missions, toss some grenades, or drop some equipment to empty your hands quicker.
There are no benefits to carrying less weight than the maximum carry capacity, and especially it is unnecessary to carry more than the maximum carry weight which merely causes the mentioned TU penalty.