why is budgie shaking?

  my budgie also poops green poop and shakes a lot and even fell of his perch today but got up in the end also he has lost a lot of weight
Since birds hide their illnesses as long as they can, by the symptoms you describe he could be near death. Take him to the vet immediately.
My budgies shake quite a lot too I thinks it normall as I have had them more over three years and they seem to be very active but I have never seen them lost weight and this seem very odd to me.I suggest you ring up a local vet and seek for advice.
The green diaharrea is indicating your bird is sick, get him to a vet! If he fell off his perch That means he is getting weak and will DIE SOON!
The budgie is obviously scared of you. You should buy another budgie to accompany him.
My grandad's budgie had the same thing, and the vet said it was a possible stroke. He said they get over it by themselves.
Maybe he needs a sweater?