Ok after some man curl
digging, I think I've found out the answer, though I'm not 100% sure about it's validity:
-w, --write-out <format>
Defines what to display on stdout after a completed and successful operation.
[...]
The variables present in the output format will be substituted by the
value or text that curl thinks fit, as described below.
All variables are specified as %{variable_name} and to output a
normal % you just write them as %%.
[...]
size_request The total amount of bytes
that were sent in the HTTP request.
size_upload The total amount of bytes that were uploaded.
That means adding a -w '%{size_request} %{size_upload}'
and then adding the resulting numbers in the output after the request will give you the request size in total.