While I know that it depends a lot on the taper, I was wondering whether anyone ever tried to work out the approximate weight changes with increasing line length to properly load the rod.
E.g. if your your rod loads well with a 45' line @ 550grain, how much should a 55' and 65' head weight to load the same rod...
Well, why do you want to know ?
For a given taper design, it's a relatively straightforward exercise in integral calculus to figure this out, but, why?
For lines that have level back tapers -- some of the more recent NextCast lines, many comp lines -- it is even more simple : measure the head at the back, convert to gr/foot (tables in Al Buhr's book), multiply by # of feet in length change.
In my experience, this is a useful thing to know pretty much only if you have customized a line for a given rod, worn out the line, and then want to cut exactly the same line to the same specs as the first line. Even then it's only an approximation, due to manufacturing variation.
You can get approximations from the AFFTA tables for line weight class vs. head length. That's probably the most general thing you'll find.