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I have been working on a question, and my lecturer has hinted me with this equation that doesn't include forces due to weight?

$C_{M_x}=C_{M_{ac}}+C_L(x/c−x_{ac}/c)$

What he told us was that due to the derivation of the equation we can ignore weight with this equation? However when taking the moment of course one must take weight into account correct? Is it included in the lift coefficient?

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These are the dimensionless coefficients. The equation computes the $C_{m_x}$ at some point not at the aerodynamic center by adding the $C_{m_{ac}}$ to a (nondimensional) force times a (nondimensional) distance. Note that the $C_{m_{ac}}$ is independent of angle of attack. To the first order, it is a function of the camber line. But the $C_l$ is a function of angle of attack. So the $C_{m_x}$ varies with angle of attack.

If you are looking for where the weight is "hiding", changes in weight are reflected in changes to $C_l$ in level flight.

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