The longer it stays around do they normally get weaker?
A particular viral particle doesn't get weaker - an alpha always has alpha virulence, a delta always acts like delta. When we talk about how much virus is "out there", we're really talking about a mixture of alphas, betas, deltas, omicrons and other variants. In March 2020, the predominant variant was very virulent and very contagious, but as it mutated, and the mutations spread, other variants in the mix began to predominate.
If omicron spreads easily and causes only mild disease, then it may become the dominant coronavirus in that mix, so we might think of it as "coronavirus became weaker", but it's really just a change in the proportion of variants in the mix.
(This is somewhat similar to the different flu variants that predominate every year, necessitating new vaccines.)