I cannot select bones once in weight paint mode. I have already turned off "Lock object modes" and I can switch between pose mode and weight paint mode so that's not the issue. I can go into pose mode and move my mesh around so I know it's parented and I know it has an armature modifier. I am not sure what I am doing wrong. Here is a link to download the file. I am using the latest version of Blender at the time of writing this 2.82
https://mega.nz/#!QUpljRYQ!kFUGNKmHashr6CYRD-hbAy9V3pSqacHfjZB7C1xzXdg