Question

How is the weight moving between X=6 and X=7.5?

Answer 1

It would be moving 1.5 unp and down because the volume constant 

Answer 2

Have you looked at the graph ? ?

The weight is at the rest position of the spring and moving upward
when x=6.

During the next 1.5 seconds, it moves up to the upward limit (the
'amplitude' of the oscillation) and then back down to the rest position.

When x=7.5, the weight is back at the spring's rest position, and moving
downward.