This addon allows you to adjust weights without leaving Edit mode. It allows you to use all face/edge/vertex selection tools so you can weight paint more easily.
This add-on will only appear in Edit mode. It's called "Adjust Weights" and will be under the 'Measure' tool in the main left hand toolbar.
Download weight_painting.py
Edit -> Preferences -> Add Ons
Click Install
Select weight_painting.py and click Install