Main Entry: 1rack
     Pronunciation: 'rak
     Function: noun
     Etymology: Middle English rak, probably of Scandinavian origin; akin to Swedish dialect rak  wreck; akin to Old English wrecan to drive -- more at WREAK
    Date: 14th century
    : a wind-driven mass of high often broken clouds
 

     In this phrase: "...weather'd every rack..." Walt Whitman is talking about how the ship has survived every hardship, every gust of wind, every dangerous happening.  The ship is representing the American people, the whole nation.  Divided by the Civil War, America (the ship) has to overcome many obstacles, (which are represented by the word rack) in order to restore America to peace and unity.

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