What is the difference between weeks, weeks' and week's?

MS grammar keeps giving me the blue squiggly when I type the following:

I am available most of the time with about a weeks notice.

It wants me to change it to: weeks' notice or week's notice.

Which should I use, and why?

You need to use a possessive form. Either singular if you are talking about one week or plural if you are talking about more than one week.

We form possessives by adding "apostrophe s" to the end of a singular. To form the possessive of a plural (which already ends in "s"), we just add an apostrophe.

It should be "a week's notice".