Gord Beaman wrote

I've never heard of this. Any a/c that I'm familiar with
certainly don't modulate takeoff power according to their weight.

It can be done for most all jet transport category aircraft.
It is called the "reduced takeoff thrust" procedure. Most
airlines have FAA approval to use this procedure in order
to extend engine life. It's all about "creep units", RPM,
and EGT or TIT. Keep the RMP and EGT as low as possible for
extended engine life.
It goes something like this......
From the runway takeoff limit chart, determine the maximum
allowable temperature for the actual weight. Then use that
assumed temperature to determine the takeoff power setting.
This will produce takeoff performance equal to a takeoff at
maximum weight for the actual temperature.
I'll scan the procedure out of my Boeing manual if this is
not clear enough.

Bob Moore
VP-21 VP-46
ATP B-707 B-727
PanAm (retired)