It has been known for a long time that graphene flakes of certain geometries can develop spontaneous spin polarization. Here, it is studied what happens when two triangular graphene nanoflakes, possibly different sizes, are placed in close proximity with AB (Bernal) stacking. The results of first-principles calculations show that the magnetic ground state of the bilayer system depends on the different sizes of the two nanoflakes, and spinrelated energy gap can be controlled with external electric fields. Under certain circumstances, the system even can be tuned into half-metallic nature, which might potentially be exploited in future spintronics applications.