Think in terms of angle of attack. In general terms, there is one optimum AoA for max range regardless of weight. That means a heavier aircraft has to fly faster than a lighter aircraft to achieve its optimum AoA. Since more of the available thrust is needed to achieve a higher TAS and to support the heavier aircraft, the optimum altitude will be lower (and TAS higher) than for a lighter aircraft.
Another factor coming into play might be Mcrit. Assuming the heavier aircraft has enough thrust to keep climbing, the corresponding TAS for its optimum AoA would keep creeping towards Mcrit. So, somewhere will be a design trade-off between thrust, drag, speed (limits), AoA etc.