Weight painting is more art than science. Blender's automatic weights work decently well but almost always need some touching up. There are many YouTube videos on how to clean them up
That process is usually going to pose mode and putting the character into a good position to spot problems, (bend arms, knees, head, etc) then changing to weight paint mode to clean them up.
To do that you click through the vertex groups for each bone name and paint more or less influence on the body. So "Head" vertex group you'll paint the head all red, and maybe a little neck too, etc and continue through the body doing that for each bone.
Weight painting is inescapable in game dev and animation. If you add clothes, hair, jewelry, shoes or any other items to any model, you'll need to weight paint those new additions too. So best to just learn the basics of doing it.