As adjectives the difference between aloof and eccentric
is that
aloof is reserved and remote; either physically or emotionally distant; standoffish while
eccentric is not at or in the centre; away from the centre.
As an adverb aloof
is at or from a distance, but within view, or at a small distance; apart; away.
As a preposition aloof
is (obsolete) away from; clear of.
As a noun eccentric is
one who does not behave like others.