Hi Nathi,
That panel only shows the weights for the active vertex (essentially only 1 vertex at a time)
When you change the values, it will only change that 1 vert as well. You can use the paste, and copy operators to edit all the selected vertices though.
However, you probably don’t want to do that when you have an edge loop selected length wise. That will require a bit of clean up – but it’s worth testing everything out on the simple example so all the ins and outs become more familiar.