Essential Tremor: This is the most common cause of tremors in adults, characterized by a progressive, bilateral, and symmetric tremor, often affecting the hands. The patient's age, lack of other symptoms, and the nature of the tremor make essential tremor a likely diagnosis.

Parkinson's Disease: Although less likely given the absence of other parkinsonian features such as bradykinesia, rigidity, or postural instability, early stages of Parkinson's disease can present with tremor. The patient's age and the bilateral nature of the tremor keep this in the differential.
Anxiety-Related Tremor: The patient reports mild anxiety, and anxiety can exacerbate or cause tremors. However, the progressive nature of the tremor over months suggests a more chronic condition.
Hypomagnesemia: With a magnesium level of 1.3, the patient is hypomagnesemic. Magnesium deficiency can cause tremors among other neurological symptoms, making this a potential contributing factor.

Hyperthyroidism: Although the patient denies recent medication changes or symptoms like palpitations, hyperthyroidism can cause tremors and should not be missed due to its potential for serious complications if untreated.
Medication-Induced Tremor: Despite the patient denying recent medication changes, it's crucial to review all current medications for potential tremor-inducing effects, as some medications can cause tremors even at stable doses.
Wilson's Disease: A rare genetic disorder that can cause tremors, among other symptoms. It's more commonly diagnosed in younger individuals but should be considered to avoid missing a potentially treatable condition.

Fragile X-Associated Tremor/Ataxia Syndrome (FXTAS): A condition affecting older males with the fragile X premutation, characterized by tremor and ataxia. It's rare but should be considered in the differential for older males with progressive tremor and ataxia.
Spinocerebellar Ataxias: A group of genetic disorders that can cause progressive ataxia and sometimes tremor. These conditions are rare and typically present with more prominent ataxia than tremor.
Neurodegenerative Diseases (e.g., Multiple System Atrophy, Progressive Supranuclear Palsy): These conditions can present with tremor among a constellation of other symptoms. They are rare and often diagnosed after other more common causes have been ruled out.