Hairs that fall out are narrower at the base

If most of the hair that falls out is noticeably thinner at the base than it is on the end, does this most likely mean that many of my follicles are miniaturizing or is this just the natural hair process and likely nothing to be too concerned about?

Yes, as hairs become more and more miniaturized, as they grow they become thinner and thinner so if and when they fall out, the base will be the thinnest part of the hair shaft