What are the units of 85000 Molecular Weight of a polymer
First of all $M_w$ is not the number of monomers in a chain of PVA. The number of monomers in a chain is called the degree of polymerization.
$\overline {M_w}$ is the weight average molecular weight. It is a way of determining the molecular mass of a polymer. As polymer molecules have different chain lengths, the average molecular mass will depend on the method of averaging. For example, we can use the number average molecular weight which is based on different type of averaging.

As for the unit, it's as you mentioned: g/mol. In biochemistry, they use the dalton (Da) as a mass unit for biopolymers (1 $N_a.$Da= g/mol, where $N_a.$ is the Avogadro number). So, when we say a protein has a molecular weight of 64000 g·mol$^{−1}$, it has  also a mass of 64 kDa.

P.S. To be rigorous, we have to say ** molecular mass** instead of ** molecular weight**. But this was an old way of naming things.