There is a lot of research on the persuasiveness, or otherwise, of so-called "hedge words" — words that qualify a statement or make you sound equivocal (such as "possibly" and "probably"). Most research I have read recommends eliminating hedge words, where you can. More nuanced research suggests that qualified statements can be more persuasive than unqualified statements, depending on your audience. For example, if your reader knows and is interested in your subject, then qualified statements may persuade them more than unqualified statements; however, for people who do not know your subject or who are uninterested or who are too busy to really pay attention, then hedge words can deplete the strength and meaning of your message. Here is a list of hedge words to think carefully about.
It may sound counter-intuitive, but using emphatic language can sometimes weaken your argument rather than strengthen your argument. By contrast, understatement has much more persuasive force. Look at the following list of emphatic words and phrases and think about whether you really need them in your writing.