That doesn't mean we should use them when we're writing. These words have become meaningless from overuse. They are vague, or they may be as superfluous as the "Umm" that we all say and never write (except sparingly in dialog).
For instance, the word "very" is useless. I can say my character is "angry" or is "very angry". It doesn't change what the reader sees. The reader sees that my character is angry. Even "a little angry" doesn't help the reader. Your character is angry or not.
Other words, like "went" just don't convery as much information as the reader wants.
Saying "Joe went into a room" doesn't tell the reader as much as saying "Joe scrambled through the doorway" or "Joe sidled around the corner".
"That" is overused. It's sometimes necessary, but usually it's just an extra word that slows your reader down.
The weak word analysis highlights the commonest weak words so you can see where your prose needs to be cleaned up. This might be deleting words or finding more descriptive synonyms.
Here's a not-horribly-bad paragraph that's full of weak words:
Some of these words were simply superfluous, some could be replaced with stronger words. The reworked paragraph still has one weak word, but not so many that it's wishy-washy.