Hardly

From hard + ly.

Full definition of hardly

1603, John Florio, translating Michel de Montaigne, Essays, Folio Society 2006, vol. 1 p. 148:Let him hardly be possest with an honest curiositie to search out the nature and causes of all things ....

(manner, archaic) Harshly, severely.
I can't really deal hardly with people.
(now rare) With difficulty.

1603, John Florio, translating Michel de Montaigne, Essays, Folio Society 2006, vol. 1, p. 234:And what gentle flame soever doth warme the heart of young virgins, yet are they hardly drawne to leave and forgoe their mothers, to betake them to their husbands ....
1977, John Le CarrÃ©, The Honourable Schoolboy, Folio Society 2010, p. 40:While in Chelsea, Anne Smiley pined, taking very hardly to her unaccustomed role of wife abandoned.

2011, November 3, David Ornstein, Macc Tel-Aviv 1-2 Stoke, With this the second of three games in seven days for Stoke, it was hardly surprising to see nine changes from the side that started against Newcastle in the Premier League on Monday.
2013-07-06, The rise of smart beta, Investors face a quandary. Cash offers a return of virtually zero in many developed countries; government-bond yields may have risen in recent weeks but they are still unattractive. Equities have suffered two big bear markets since 2000 and are wobbling again. It is hardly surprising that pension funds, insurers and endowments are searching for new sources of return.

they hardly ever watch television; I hardly think they'll come in this bad weather; it's hardly possible he could lose the election.

In the sense "barely", it is grammatically a negative word. It therefore collocates with ever rather than never.

Compare example sentence with I almost never watch television