For S&L cruise at a given airspeed, static CG, higher weight requires a higher lift coefficient, and so a higher angle of attack.
Power has to match drag at the new drag coefficient. So how much does the drag coefficient change by?
For a 'typical' aerofoil at cruise speed, not much.
for example:
File:CL, CD NACA632618.png - Wikipedia, the free encyclopedia
from
Drag Polar - Wikipedia, the free encyclopedia
Of course, some aerofoils may not be 'typical'
