The weird thing is that I can't replicate this issue it in Sketch for example. If I type 2 letters in that font, and select one and change the weight, the kerning does not jump. In Illustrator the kerning also seemed off, unless you use optical kerning.
Also, we spoke to the type foundry who made the font, and they said their programmer made the same kind of animation using CSS and JS, and they didn't have this issue. But I didn't get the change to verify this.
Anyway, the cheat with adding a small number seems to do the trick. I wrote a little function, which checks the text beforehand and applies custom minus kerning to know pairs. The designers who are going to work with this code can easily use this same function to overwrite values they don't like. Works for now.
Also, we have a plugin for After Effect that does the same kind of animation, and also doesn't do the kerning jump (could be using optical kerning). But the plugin has some other flaws, and is not user friendly, hence we built our own code to create the typographic animations we need
Thanks again for your time and thinking with me