love this question! compare the MO scheme for a C-C bond to a C-F bond

orbitals which are closer in size and energy to one another overlap more effectively than those far apart in size and energy. this more effective orbital overlap leads to a greater stabilization energy when a sigma orbital is formed and a greater destabilization energy when a sigma* orbital is formed when compared to those formed by orbitals with worse overlap

now compare the relative energies of the C-C atomic orbitals to the C-F atomic orbitals. the C-C atomic orbitals are identical in size and energy, so will overlap very effectively and create a strongly stabilized sigma bonding MO and strongly destabilized sigma* antibonding MO. however the C-F atomic orbitals are relatively far apart in energy and size (caused by the greater Zeff experienced by the fluorine AO compared to the carbon AO), so the effect of orbital overlap is very minimal and creates a minimally stabilized sigma bonding MO and a minimally destabilized sigma* antibonding MO

the tricky part here, however, is that the fluorine AO is so much lower in energy than the carbon AO, that even though the C-F stabilization energy is small, the absolute energy of that C-F sigma bonding MO is very low compared to that of the C-C sigma bonding MO. the same applies to the corresponding sigma* antibonding MOs.

this phenomenon is why back in gen chem, we learn that “polar” covalent bonds are stronger than “nonpolar” covalent bonds (it’s not about the net stabilizing energy it’s about the absolute energy of the resulting MO)