Ok, your problem is simple.
The reason your vertex groups do not take is, that you applied them all on the main hull of the ship. If your ship pieces are still separate objects, the vertex groups for the bone influences need to be on THAT object.
For your ship, you won't need to create them by hand. Parenting to Bones will do it for you.
Clear up your parenting structure, so one object does not move the other. Just hit Alt + P to clear Parents with "Clear and keep Transformation"
You need to apply the transformations to the objects, that you made in Object Mode. Your Location Values should be zeroed out, the scales should be at one.
Select Bone in Pose Mode
Click on Geometry you want the Bone to be the Parent of
Shift-Select the Armature again
Ctrl + P to Parent the Geometry to the Selected Bone
Selecting one bone of the armature (in Pose Mode), like for example the one that controls the landing gear, you select the mesh you want to attach to it to, Shift Select the Armature again and then hit Ctrl + P and Parent to Bone.
I have done this for you in the blend file. I would also advise you to roll your bones over, so that all hatches close by rotating the x-axis, just to give an example. That will allow you to lock the other transform channels. Otherwise, you will go nuts animating.
I have also set your rotation to ZYX Euler. Since the hatches only rotate around a single axis, that will make everything easier, transforming, reading and changing the animation curves, locking the right channels. Try it, you will see it right away.
