Essential Tremor: This is the most common movement disorder and often presents with a progressive bilateral hand tremor, typically affecting individuals over the age of 60. The absence of other neurological symptoms and the specific characteristics of the tremor (e.g., action or postural tremor) support this diagnosis.

Parkinson's Disease: Although less likely given the absence of other parkinsonian features such as bradykinesia, rigidity, or postural instability, it's still a consideration, especially if the tremor is resting rather than action or postural.
Anxiety-Related Tremor: The patient reports mild anxiety, which can exacerbate or contribute to tremors. However, the progressive nature of the tremor over two months might suggest a more structural or neurodegenerative cause.
Hyperthyroidism: This condition can cause tremors, among other symptoms. Although the patient denies recent medication changes or other symptoms like weight loss or palpitations, it's still worth considering due to its potential impact on the nervous system.

Multiple System Atrophy (MSA): A rare neurodegenerative disorder that can present with tremors, among other symptoms like autonomic dysfunction and ataxia. It's crucial to consider due to its poor prognosis and the need for early diagnosis.
Wilson's Disease: An inherited disorder that leads to copper accumulation in the body, affecting the brain and liver. It can cause tremors, psychiatric symptoms, and liver disease. Although rare, missing this diagnosis could have severe consequences.
Stroke or Transient Ischemic Attack (TIA): While the patient denies recent trauma or falls, a small stroke or TIA could potentially cause a tremor, especially if it affected motor control areas of the brain.

Fragile X-Associated Tremor/Ataxia Syndrome (FXTAS): A condition affecting older males with the fragile X premutation, characterized by tremors, ataxia, and cognitive decline.
Neurodegeneration with Brain Iron Accumulation (NBIA): A group of rare, inherited disorders characterized by progressive neurological deterioration, often with tremors, and brain iron accumulation.
Whipple's Disease: A rare, systemic bacterial infection that can cause a variety of symptoms, including tremors, weight loss, and cognitive changes, due to central nervous system involvement.