In this answer, Bianfable notes:
[O]ptimum cruise altitude for a 777-200LR at a weight of 340 t is only FL285, but after burning 100 t of fuel it has increased to FL360
Why is that? Is it simply the momentum of the heavier plane is able to reduce the effect of drag? Is it linear, or stepped? And, does the plane rise at some point to the higher level (assuming on a long trip)?
FreeMan suggests in comments it may be the Angle of Attack (AoA) that makes a difference - higher AoA for heavier planes means more drag, so better off at higher altitudes.
As ymb1 notes in comments, from their earlier question, I wonder about this sentence:
At higher altitude the friction and pressure drag is lower but the induced drag is higher, so increasing the mass will cause a much higher jump in drag.
That makes me wonder if it's more related to the different components of drag, than the AoA (or just the AoA, maybe it's a combination of both?)
+1for researching it. I asked a very related question, and I think the answer here will help, but the terms used may be too technical. If they are, as a suggestion, you can edit your question to include the additional points being discussed about. But I don't think it's a duplicate of yours. $\endgroup$