Interesting question. I like Lemurian's approach of using Breguet's range formula to assert that take-off weight / landing weight is effectively constant. However I'm not sure it really gets at the heart of Keygrip's question as to why this is an issue on the 777 but not the C152. Let me look at the problem from a different angle.
The key parameter is the % increase in power required per % increase in weight, which I'll call alpha. Mathematically that's
(dP/P) = alpha * (dW/W)
Knowing that, and assuming that fuel consumption is proportional to power required:
Extra fuel consumption rate / Normal fuel consumption rate = alpha * Extra fuel loaded / Weight
Rearranging that:
Extra fuel consumption rate / Extra fuel loaded = alpha * Normal fuel consumption rate / Weight
The left hand side is just the proportion of the extra fuel burned per hour. It depends on (Normal fuel consumption rate / Weight), so it's more (per hour) for a short flight than a long one, but I don't think that goes far towards explaining why it's significant for a 777 but not a C152.
What about this factor "alpha"? Well that will depend on how much of the drag is lift- (and therefore weight-) dependent. That depends very strongly on the speed you fly at.
At minimum drag speed, half the drag is weight-dependent induced drag. As you increase the speed, weight-dependent induced drag becomes a much lower proportion, and % extra power required per % extra weight is much lower.
If I take a drag polar that looks like (^2 is "squared")
drag = W^2/v^2 + v^2
then I get
alpha = 2/(1 + v^4)
where v is the speed relative to minimum drag speed. That's a really strong dependence on v. At minimum drag speed alpha is 1. At 1.4 times minimum drag speed, alpha has fallen from 1 to 0.4. At 1.7 times minimum drag speed, alpha has fallen to 0.2.
I don't fly big jets but I think that's where the difference lies between them and light aircraft.
My light twin burns about 85 lb/hr at 3400 lb, so my proportion of extra fuel burned per hour is alpha * 2.5%. But that's cruising at about 50% above minimum drag speed, so alpha is about 0.3, and it costs me less than 1% per hour to tanker fuel.
If I'm interpreting the Boeing figures I've got here for a 757, and cost index 0 is a reasonable indication of minimum drag speed, even cost index 70 suggests a cruise speed just 1.07 faster. At today's lower cost indices, that might be even 1.05 times minimum drag speed, and so alpha is going to be pretty close to 1 (say 0.9). I appreciate my naive drag polar might not be accurate at Mach 0.8, but the point stands that you're flying at a speed where weight dependent drag is a much greater proportion.
So do get back to Keygrip's question, it starts to matter to a significant extent when you start flying at speeds closer to minimum drag where weight-dependent drag is a significant proportion of total drag. That tends to apply to fuel-conscious ops in big jets, and less to the always-cruise-at-75%-power C152s.