Freezing the modeling history of an envelope also freezesremoves the weight

To overcome this, don't just select the object and click freeze. In the explorer, set the envelope operator on the top, above all the modeling operators (by dragging it on the first modeling operator). Select the modeling operator right underneath the envelope op, click freeze (lower right). The weight is preserved.
You should use freeze often in order to avoid conflicts and to simplify the scene thus accelerating playback.