There are a couple of considerations which could throw off your measurements.   One is, “exactly how is the figure of ‘amount of memory used by process X’ calculated?”   The other is, the copy-on-write functionality (like everything else in the virtual memory subsystem...) happens in terms of pages, and will respond to any change to that page, whether that change is considered by you to be “inconsequential” or not.

COW does work in terms of memory pages.   The page-tables of the child process are set to point to the pages of the parent, but they are flagged to cause a page-fault if the page is subsequently “touched.” When that kind of page-fault occurs, the page is copied.   That is a very coarse level of granularity:   the size of a page.

COW is a common feature of operating systems these days.   You should be able to assume that it is being used, and that it cannot be turned-off.