Sometimes when one encounters others, they try extra hard to convince you of their honesty. The thought is that if they need to work extra hard to convince you of this, rather than letting their reputation and/or the way that they carry themselves convince you of this, then should perhaps consider them untrustworthy.
Naturally enough, this is very context sensitive. Younger people are more prone to try to oversell something, so they might be given special dispensation. If one is caused of a heinous crime, hopefully an innocent person would protest strongly.
Perhaps the general thought is that people of low character do not realize that one’s bearing and reputation are assets in this cases, and as such, try to convince the only way they know how. Perhaps commenters will state other theories.
So try to build a reputation for honesty; also be of honest character, hopefully this will come through in your bearing such that others can see it.
As an example of protesting too much, consider the case of former UN Ambassador Susan Rice. She has a reputation for being a liar, as evidenced by her parading around the Sunday discussion news shows deliberately lying about the cause of the Benghazi fiasco. At the end of the Obama Andmisitration, as the principles were plotting to investigate Trump and associates, she wrote and sent emails to herself to document to what was happening. Who does that kind of thing? Obviously they were for future public consumption. In one email she makes a big profession about doing everything by the book. Spoiler – it wasn’t.
Short Answer – be on the lookout for people protesting their honesty/innocence a bit too much, or in an awkward manner.
Exit Question — How much is honesty worth?