Is it true that insects hitting the fuselage could decrease aircraft performance and increase fuel consumption? Insects are small in mass. I think even a large amount of them accumulate on the aircraft's outer skin, it wouldn't be significantly enough to affect fuel consumption.
You're right, insects are very small, so they influence things which happen on their scale. The one important phenomenon on an airliner which has the scale of insects is the boundary layer, the sheet of air around all wetted surfaces where air speed changes from zero (relative to the plane) to the speed it has at some distance. This is called the boundary layer. Its thickness changes from zero at the stagnation point to several centimeters at the end of a long fuselage.
What does the boundary layer look like?
At the leading edge, the boundary layer starts with a thickness of zero. Now friction with the wing will cause some air molecules to be slowed down, and soon you get a sheet of air in which the molecules closest to the aircraft's skin will move with the skin, and the more you move away from the skin, the less they are slowed down. Initially, the layers of air within the boundary layer show no cross movement of molecules. Compare it with a multi-lane road with bumper-to-bumper traffic where no car changes lanes. Since all molecules move along their layer of air, this is called laminar flow (lat. lamina = layer).
At some point downstream oscillations will develop, and once they become unstable, molecules will move between the layers of air. Now you have faster ones from more distant layers moving closer to the skin and kicking the slow ones there ahead, and slower ones from close to the skin moving away, slowing down the more distant layers. Now the cars in your multi-lane road cross lanes, and the result is that all lanes but the rightmost one will move at similar speed. Since the cross-flow is the result of turbulence, this boundary layer is called turbulent.
Speed profiles of laminar (left) and turbulent (right) boundary layers. Image source.
Consequences for drag
The cross flow causes the turbulent boundary layer to have a much steeper speed gradient at the aircraft skin, causing much more friction drag. At the same time, more energy is taken from the flow due to friction, so the whole boundary layer becomes thicker. If you look at the local friction drag, the parameter plots made possible by XFOIL are quite illuminating.
Friction drag over chord for an E502mod airfoil at 3° AoA. Blue: Top surface, Red: Bottom surface.
The plot shows the friction over chord for an airfoil at 3° angle of attack. All flow is attached (save for one small separation bubble on the bottom near the transition point). Can you spot the transition points from laminar to turbulent flow? Yes, it's where the friction drag jumps up and stays annoyingly high downstream. Note that the flow around an airliner's wing happens at a much higher Reynolds Number, so the transition points are closer to the leading edge than in the plot above. I chose the low Reynolds Number in the plot above because it shows the phenomenon more clearly.
But you see also a friction spike at the nose! This is caused by the very small thickness of the young boundary layer. Even though it is laminar, it shows a high friction contribution simply because it is still very thin. Now imagine you have both effects, a thin boundary layer and the bigger friction of a turbulent boundary layer, added together. This is what bugs at the leading edge of the wing will give you! They make the wing's surface rough and drive up friction losses due to an early transition of the boundary layer into turbulent flow.
Consequences for maximum lift
But there is also a second effect: The longer the boundary layer develops, the more the flow loses the ability to slow down and increase pressure towards the trailing edge. A flow's energy is either speed or pressure, but if the energy of the flow is sapped by friction, none of both is left when needed to negotiate the last half of the wing's shape. The flow will separate earlier if it had been turbulent from the beginning, and the wing will stall at a lower angle of attack. This is the second negative consequence of bugs on a wing. It can be mitigated by careful airfoil design, but then this airfoil will show lower bug-free performance.
Glider pilots know this very well, especially those who flew planes which used the Wortmann FX 67-170 airfoil. It had excellent L/D without bugs, but both rain and bugs converted the plane to something resembling a brick. I once flew a Janus B into a shower, and minimum speed increased from 80 km/h to 110 km/h. A few seconds of flying at higher speed cleaned the wing, but then it was time to land, because I had lost so much altitude.
The issue here is not the additional mass or weight, but the disturbed airflow over the wings. The key terms here are laminar flow and turbulent flow.
The below picture will show normal laminar and turbulent flow over a wing. With insects or other dirt on the leading edge, the transition will happen closer to the front, leading to a decrease in performance.
(Image Source: www.allstar.fiu.edu)
The NASA has done some reasearch too:
Anyone who has driven through a cloud of insects knows how quickly the bug guts build up on the vehicle, causing problems with visibility, clogging the air intake and radiator, and ruining the car's exterior finish.
The problem for an airplane is that its aerodynamic design is meant to have air move very smoothly across the body and wing surfaces, which is called laminar flow. When there is a disruption in that laminar flow, such as from the accumulation of dead bug parts, you induce the opposite of laminar flow, which is turbulence.
Finding ways to maintain laminar flow through all phases of flight is a big deal for the aviation community because it could save millions in fuel cost, while also reducing the amount of noxious emissions released into the atmosphere.