Can a bad/failing battery cause an alternator not to keep up?

[dbjunior 10+ year member]

It takes more effort to turn ho alts so a good and tight belt is needed this happens all the time on heavy bass notes it will slip more

 

[Sephious 10+ year member]

It takes more effort to turn ho alts so a good and tight belt is needed this happens all the time on heavy bass notes it will slip more

The belt is definitely tight on there, and I can't make it any tighter. My tensioner is spring-loaded and does the tensioning itself.

Also: I have checked my grounds. They're good.