Green’s Dictionary of Slang

to a great or excessive degree, esp. unwisely.

1854		G.J. Whyte-Melville General Bounce (1891) 185: That officer has dined ‘severely,’ as he calls it, and is slightly inebriated.
1932		‘Ex-Légionnaire 1384’ With the Secret Service in Morocco 30: [S]ave to shove more bottles of wine in front of him, I left him severely alone .
1956		J. Curtis Look Long Upon a Monkey 69: Everything’s severely under control.
1987		Eble Campus Sl. Oct. 5: severely – very much.