genomics - DNA methylation and genome size

Is there any relationship between DNA methylation as a level of
stability to epigenetic states and genome size?

I would say yes, because methylation is used to disable genes in differentiated cells. Disabled genes in differentiated cells generally need to stay disabled to maintain normal behavior for the cell type. Larger genomes usually encode more different types of cells.

it is claimed that DNA methylation is not required for epigenetic
stability in Drosophila melanogaster and yeast, both genomes much
smaller than mammalian or plant genomes.

According to my book (S377 molecular and cell biology, book 2, p140) Drosphila don't need methylation because they perform transcriptional regulation by persistent chromatin remodelling instead. Yeast being single celled would have less need for this type of control.

Could it be that DNA methylation is needed to help activate/repress certain genomic regions on top of other epigenomic marks when the genome is so vast that there is a need for an extra level of marking?

It is used as a repressor because it inhibits hydrogen bonding of transcription factors and the like. I have not heard of it functioning as an activator.

There are also other uses for methylation, for example newly synthesized DNA is hemimethylated - where the parent strand is methylated and the child one not. From this it can be determined which is the parent strand during DNA repair.