What is the physical/deeper reason for the second order shift of the ground state energy in time independent perturbation theory to be always down?

I know that it follows from the formula quite straightforwardly, but I could not find a deeper reason for it even if if I took up examples like the linear Stark effect.

Would you please tell me why?

Much obliged.

What is the physical/deeper reason for the second order shift of the ground state energy in time independent perturbation theory to be always down?

I know that it follows from the formula quite straightforwardly, but I could not find a deeper reason for it even if if I took up examples like the linear Stark effect.

Would you please tell me why?