What diseases can have an result of weight loss or uncontrollable shakiness?

Many. Diabetes, cancer, thyroid problems to name the few, see doctor, they will get your medical history and do physical exam and hopefully order an appropriate tests to find out for sure.
Hyperthyroidism. Thyroid hormone=hormone of metabolsim and hyperthyroidism=excess of thyroid hormones. Your body is basically revved up 24/7 thus consuming more energy and resulting wt loss. Jitteriness/tremor can a a sign, as well as heat-intolerance. Please consult doc to get treatment as untreated hyperthyroidism can cause serious problems for you. Good luck.