Answer
The support force on the crate decreases. The support force on the workmen's feet increases.
Work Step by Step
The support force on the crate decreases as it is lifted, and presses with less force on the floor. If it were sitting on a scale, we would see the reading decrease until the crate were entirely free of the floor, at which point the reading, and thus the support force from the floor, is zero.
Meanwhile, the support force on the workmen’s feet increases as they gradually pick up the crate. When the crate is off the floor and at rest, its weight is completely transferred to the workmen, whose normal/support force increases by a combined amount equal to the crate's weight.
