The old post just above yours kinda goes into this ... here it is explained a little differently (FYI, in the 1980's I worked in AA's "Load Control" ...Weight & balance calcs ... I'm sure procedures have changed over the years, but the concept is still there) ...

The FAA approved method for "Weight & Balance" calculations allow airlines to use specific FAA weights for passengers and bags instead of weighing everybody and every bag.
So passengers weigh "x" pounds. The FAA value for "x" includes a carry on.
Likewise, each bag weighs "y" pounds. Airlines do count each individual bag loaded (more specifically, for "balance" purposes, they count how many bags in each compartment).

When the Gate Agt "converts" a bag from "carry-on" to "checked", the fixed value of "x" for that passenger does not change, yet the bag count increases by one, thus increasing (on paper) the take-off weight by "y" lbs.