Dependence of tension (considering a pulley system) on the mass of loads

Consider the diagram below

All circles are pulleys, which are fixed at the ceiling. M represents an engine (with a certain power) that is pulling the cable. C and D are weights. The acceleration of the system is 0 (D is moving with constant velocity). Assume the pulley and the rope have no mass, and friction is negligible.

One can calculate the tensions on the pulley from which C hangs by diving C's weight by 2. However, the tension also depends on the mass of D, right? The previously mentioned calculation doesn't take this into account.

My question is, if the mass of D varies, what happens to the tension on the left cable? Does it remain constant and it is the engine that has to compensate for the variation of mass? Or does the tension vary?

If the mass of $D$ varies and the mass of $C$ and the power from $M$ remain constant, the system would likely begin to accelerate one direction or another, meaning that the tensions in the pulleys suspending $C$ will have a different tension than $T=\frac{M_C g}{2}$, which would also likely give a non-constant tension, since the power of $M$ is being kept constant, not the force, and as the speed $v$ (or the angular speed $\omega$ for a spinning motor) increased, the force $F$ (or torque $\tau$) would have to decrease to hold $P$ constant or vice versa if the speed decreased, so the masses would have to be related in a relatively special fashion in order for their speed to remain constant, which is important for the assumptions generally made in the free body diagrams drawn for such situations.