Each word or phrase in List I can be matched with a word in List II, once you determine the connection between them.

LIST I 
FEELING ILL
SEEN YOUR BEST DAYS
THURSDAY
EAGLE
ILLEGAL
NOT NOTICEABLE
LEFT WITH NO CHOICE
CLOSELY EXAMINED

LIST II
TABLE
WEATHER
MICROSCOPE
HILL
BARREL
RADAR
PAR
HUMP

HINTS:
#1: The connection hinges on two common words.
#2: The two words are opposites.

Answers:

Each word or phrase in List I can be matched with a word in List II by preceding the List II word with either OVER or UNDER:

FEELING ILL - UNDER THE WEATHER
SEEN YOUR BEST DAYS - OVER THE HILL 
THURSDAY - OVER THE HUMP
EAGLE - UNDER PAR
ILLEGAL - UNDER THE TABLE
NOT NOTICEABLE - UNDER THE RADAR
LEFT WITH NO CHOICE -OVER A BARREL 
CLOSELY EXAMINED - UNDER THE MICROSCOPE

Credit: IDEA - NY Times Crossword
Daniel A. Finan - Jan. 26, 2014
IT'S ALL RELATIVE