Final answer:
The most likely diagnosis for the patient with hypochromic microcytic anemia and skin changes is iron-deficiency anemia. Pernicious anemia, hemochromatosis, and thalassemia present with different clinical features and are less likely given the patient's symptoms and findings.
Step-by-step explanation:
The diagnosis for a 57-year-old man with weight loss, pale conjunctiva, a shiny tongue, velvety hyperpigmented plaques in the axillae and neck, and hypochromic microcytic anemia is most likely iron-deficiency anemia. The presentation of pale conjunctiva, shiny tongue, and hypochromic microcytic anemia points towards iron deficiency. The velvety, hyperpigmented plaques suggest acanthosis nigricans, which can be associated with iron-deficiency anemia.
Pernicious anemia is less likely given the scenario lacks mention of neurological symptoms and glossitis typical for vitamin B12 deficiency. Hemochromatosis usually presents with bronze diabetes and cirrhosis, while thalassemia often involves a genetic history and jaundice due to excessive destruction of erythrocytes.