What does it mean to commit weight completely?

To be totally supported on the " standing "leg.... think of walking fwd, your weight is momentarily on one leg with the body poised to take the next step .
In dance terms, there are other actions occuring, depending on the dance and the variation .

Astair. The name Andrew Sinkinson may not mean anything to you you. He is one of the top coaches worldwide. In his lecture here he had everybody do change steps down the floor. As the leg came under the body he had us lift that leg off the floor. Then out to the side and close and again lift the foot that was to move next from the floor and repeat.
For Andrew to go into such detail I think meant it is a common fault not to dance from one foot to the other. He travelled 12,000 miles to tell us that.
Is it possible to move and keep the weight in the middle, which is wrong.
Terence could tell. He probably sees it all the time. And as he said . This is not how you normally walk. Dancing is just an exaggerated walk.

In dance terms, there are other actions occuring, depending on the dance and the variation . My weight never seems to be quite there in the basic steps of the foxtrot.

Astaire. Go right back to the very Basic Steps. On this site find The International Foxtrot and go to The Three Step. Look at the little picture on the left. Take note of the straight front legs and where the weight is. Find that same frame on the video and understand how the weight is transfered to the front foot and how the knee bends as the weight arrives. Good Luck.

It is impossible to tell without seeing precisely what you are, or , are not, doing .

My educated guess would be that you are delaying the " action" of the body too long .

" body moves, foot catches ", ask your teacher to demo this .