A lot will depend on exactly which cultivar you have, but most weeping laceleaf maples will not grow upward without help. If they are stake trained when young, that will encourage their natural tendency to weep or cascade to become more upright. After 10 years, I'm not sure how much luck you will have attempting this training now.

A good many laceleaf cultivars are decribed as having a mushroom or umbrella shaped habit - they stay quite short if left to their own devices but can get very wide.

You can select a flexible limb and stake that upright. After a while, the new growth from it will weep. Then, take another flexible branch from it and stake it higher. It will take many years, but you should get it to grow taller.

If a suitable centrally located branch is selected and trained vertically up a secure stake (inserted without smashing through/barking any major roots) much greater height can be rapidly developed. If each flush of growth for the one stem is tied in then every time there is a flush the specimen will then be that much taller.

I've got an unstaked one planted in the 1960's that may just recently have gotten above waist height. New branches come out and then lay down on top of the others. Increase in height is accomplished by the branches building up gradually in layers.