Antonymy is a lexical opposition of meaning. The words are different in form and opposite in meaning. It is also a relative phenomenon (same lexical field identical in style) and it has contradictory meaning. Antonyms are a couple of words that belong to the same part of speech, share the same lexical field, similar in many respects and share all the features but one that meaning. E.g. big and red are not antonyms because they don't share the same lexical field, but tall and short belong to the same lexical field, share most of the features and differ in one dimension. Antonymy is used in lexicology as a process that defines the meaning of the word by maintaining its opposite counterpart.
Markedness is a category that operates with pairs of words which are antonyms but not lexically specified. It is definite for roots of words where there is some oppositeness. It means two members, one marked and the other unmarked. E.g. play (unmarked) - played (marked); married - unmarried. Antonymy means the positive and the negative members of a pair, e.g. old -young; beautiful — ugly; wide — narrow; How old are you?; How beautiful is she? How wide is the room? The positive members are conceptualised first and than find their antonyms. This is primary lexicalisation of the positive member of the pair. Markedness also operates in the field of derivational morphology, e.g. boy - boyhood.
Relativity of Antonymy
Small elephants are big animals. Small and big is antonymy and elephants and animals hyponymy. The antonyms are always compared in terms of a given standard; in the given example there is no absoluteness. E.g. small is bigger than big in this case.