Updating your opinion after new facts isn’t weakness. It’s your brain installing the patch.

Changing your mind in response to evidence is the system working, not the system failing. It gets read as weakness because consistency is easy to see and accuracy is not, so people who never move look solid while being quietly wrong. The alternative to updating is carrying an old error around and defending it with increasing effort.

Say it plainly when it happens. I thought that, this changed it, here is where I am now. Doing it out loud a few times makes it easier, and it tends to earn more respect than the stubbornness it replaces.