I bought and planted a weeping willow about three years ago and it is
really thriving. It's become a sturdy plant with lots of new shoots in
the spring. Trouble is, it only ever seems to grow DOWNwards! By that
I mean the branches are firmly all clumped together pointing DOWN.
When I gently take one of the newer, thinner, and thus more pliable
branches it can be lifted upwards quite a way. But of course, when I
let go it falls back down again. There is no sign that this tree/bush
on its own will ever spread upwards and seems destined to remain an
ever thicker "clump" close to the ground. (Maybe I'll add a picture to
my web site later so that readers can see what I mean.)

But is the conventional practice to train the branches, either by
staking or with guide wires? Or do I just leave the plant and let
nature take its course?

MM