If you are seeing root-stock sprouts, calling these "suckers" you will definitely want to prune those off - although "all over" doesn't sound like the usual placement. If instead this is just the normal extension growth of the cultivar it would not be desirable to cut these off. Also weeping forms look better cascading or draping to the ground - the pendent habit is the point of these - than made to look like salad bowl haircuts, or otherwise given a truncated or floating appearance.

just about everything you said ... except if they are really suckers ... is so foreign to me... that i dont understand what you want to do ...

it was never an umbrella shape.. and making it into an umbrella shape would be a crime against mother nature ..

how about you give us a pic.. and let us tell you what your goals should be ...

i have one .. growing down a retaining wall ... nothing wrong with them touching the ground ...

i would also like to confirm your ID ...

if it is a larix .... it was grafted.. and we have to make sure.. the root stock is not suckering.. because those parts would NOT be of the weeping variety ... and would need to be removed .. else they take over ... and non weeping larix can be telephone pole trees ...

see link for the forms this thing can take ... and i note.. i dont see any umbrellas ....

and do note.. i converted.. at the link.. to the latin name ... its kind of important in conifers .... [though this particular one has two latin names.. due to industry screw ups ... but it wont matter to this discussion ]

pix please .... please.. please ....

ken

https://www.google.com/search?q=Larix+decidua+%27Pendula%27&source=lnms&tbm=isch&sa=X&ved=0CAcQ_AUoAWoVChMI47-RoOj0xwIVwgySCh2CMQJl&biw=868&bih=745&dpr=0.9