Answer & Explanation
Modern is used to refer to something new whereas antiquated is used with respect to something old.
In other words, both terms are the opposite of each other.
From the above analysis, the missing word should be a word that represents the opposite of weak. Strong is used to with great influence. Therefore, the apt word is strong or any synonym of strong like potent, powerful, keen,...
Hence, Modern : Antiquated :: Weak : Strong.