Apart from a few figurative uses (such as tall order, tall story), the sense of height is the dominant one in modern English. But this sense developed quite late, in the mid-16th century.
The Old English meanings were to do with speed of activity ("quick, ready") and good behaviour ("proper, goodly, brave").
So in Shakespeare we find a mix of senses, and we need to be always on our guard. It is being used as today when Rosalind says "I am more than common tall" (As You Like It, I.iii.113). But when Bardolph describes Falstaff as "a tall gentleman", he is not referring to his height; this is the sense of "brave and bold". And the people of Illyria are not above average height just because Sir Toby says of Sir Andrew: "He's as tall a man as any's in Illyria" (Twelfth Night, I.iii.18).
When talking about boats, as in "yon tall anchoring bark" (King Lear, IV.vi.18), the word means "fine, grand". And it means simply "good, capable", when Tranio says Biondello is "a tall fellow" (The Taming of the Shrew, IV.iv.17).