I've had a dwarf weeping willow for 4 years and the branches are crawling along the ground. The tree isn't growing any taller. It's still 1' tall and stick-like as when I bought it. Otherwise, it's healthy and bushy.
Dwarf Weeping Willow
Certified GKH Gardening Expert
I would guess that at some point in time the main lead branch on the tree was damaged or even cut, with the intention of helping the tree stay small or to fill out better (very well could have happened at the nursery long before you bought it). Typically, when a lead is pinched like that, another one or two branches will take over and continue to grow up eventually, but it sounds like yours never did. Instead, it just grows out and not up. At this time, it is doubtful any of the branches will take over as a lead so it will likely never grow taller.