Font thickness is always different when I edit the text

Hi,
I'm encountering a problem on Adobe Acrobat.

Whenever I edit the texts of a PDF file, whatever the font, my added text looks bolder or thinner while having the exact same font properties (bold or not, size, etc...)

I thought this might only be a preview issue.
But even when the PDF is exported and opened in another software, we can see the difference of font thickness between the original text and the letters/words added.

I tried to change many settings related to rendering, using local fonts etc... but nothing works, even reinstalling Acrobat.
If I try to edit the PDFs with Illustrator, the added text keeps the same thickness as the original, this only happens in Acrobat, but unfortunately, Illustrator is doing a mess with the different text zones (splitting one line of text in two separate text areas for example), which makes the editing fastidious.

Thanks.