Double-clicking an object can open a Shape window, a Group window, the Convert dialog (if it's a primitive object) or an Edit mode window. It depends on the type of object you have selected when you double-click it.
The smaller window size is designed to be visually different in order to alert you that you are not in the Modeling window any longer.
There is no way to change the default window size. However, you can use the Maximize window button to quickly make the window larger.