Year by/after year?

The difference is subtle.

year after year = 年年, 一年復一年, continuously for many years; happening regularly each year
If something happens year after year, it happens regularly each year.
含有重復, 又再做意味

She sent money year after year to help the poor.

People return year after year.

year by year = 一年一年地, progressively each year
If something changes year by year, it changes gradually each year.
含有變好或變壞, progress or change

Year by year their affection for each other grew stronger.

The department has been shrinking year by year because of budget cuts.