At 16 years old, your guy is considered geriatric, so there are a few possible causes here. If he is experiencing a problem with his kidneys (extremely common in older cats), he may have an electrolyte imbalance. This may result in tremors. Other possibilities include a problem with the cerebellum, the part of the brain that controls the rate and force of motion. If the tremors seem to be worse when he is trying to do something, like eat or drink, then the cerebellum is the likely site of the problem. Diseases of this part of the brain include inflammatory processes such as an encephalitis (though generally you see other signs of illness), degeneration (possibly related to age), or an immune-mediated problem (the body's immune system attacks its own cells). Usually a steroid is needed to decrease inflammation if any of these disease processes are suspected.
Certain medications like antihistamines (Benadryl, in particular) and Reglan (an anti-vomiting drug) can also cause head tremors. Some neurologists believe that in older animals there may be some degeneration of nerve fibers which leads to tremors of the head and limbs. These tremors are not painful and don't affect the animal in any way.
I recommend, especially since you've noted a weight loss, that you have your cat evaluated by your veterinarian. A thorough physical examination and some blood work (including a complete blood cell count, chemistry panel, and thyroid level) should be performed to rule out disease processes such as kidney problems, hyperthyroidism, or liver issues, etc. If everything comes back ok, then this is probably just an age-related problem and as long as it doesn't affect his ability to eat, drink, or use the litterpan, he should do ok.
