with all one's might; to the utmost
Used to describe doing something with maximum effort, energy, or volume. Often appears as こんかぎりに or こんかぎりの.
He shouted for help at the top of his lungs.
I ran with every ounce of strength I had.
Compound of 根 (こん, 'root, source') and 限り (かぎり, 'limit'), literally 'to the root's limit'. The exact historical derivation is uncertain, but it conveys the idea of exhausting one's fundamental capacity.