  To have an analytic understanding of the higher-twist structure functions, we
calculate twist four longitudinal structure function for a positronium-like
bound state in weak coupling light-front QED. We find that in the weakly
coupled system, the fermionic part of $F_L$ is related to the kinetic energy of
the fermions and not to the interaction. We verify a previously proposed sum
rule in this limit, which in this case reduces to a relation connecting the
kinetic and the potential energies to the binding energy of positronium. Using
the analytic form of the wave function of positronium in this limit, we show
that the constituent counting rule does not hold for $x \to 1$. The twist four
$F_L$ in this limit is similar in form to a widely used phenomenological
ansatz.
