Does covid weakens the immune system?

Many viral infections transiently suppress the immune response, e.g., measles. I am not aware of specific suppression of immune system by Covid, however, some of the long Covid issues may be related to immune system. https://www.mayoclinic.org/diseases-conditions/coronavirus/in-depth/coronavirus-long-term-effects/art-20490351#:~:text=COVID%2D19%20symptoms%20can,within%20a%20few%20weeks

Yes, like other viruses, the challenge for covid is to deceive or overcome the immune system so the human DNA will be coopted to manufacture viral components'. That's how they thrive.