The phrase "burning the candle at both ends" means to exhaust oneself by doing too much, especially by staying up late and getting up early. 

The origin of this phrase is rooted in the imagery of a candle being lit at both ends, symbolizing a rapid depletion of resources (in this case, energy or time). The literal image of a candle burning at both ends conjures the idea of a candle being used up much faster than it would if burned from just one end. This metaphor effectively illustrates the concept of using up one's energy or resources quickly by trying to do too much in a short period. 

The phrase is believed to have been influenced by a similar expression in French. The French phrase "brûler la chandelle par les deux bouts" translates to "burning the candle at both ends." This phrase was used to describe someone wasting their resources or living a reckless lifestyle. The phrase was popularized in English literature in the early 20th century. One of the earliest recorded uses in English is attributed to the poet Edna St. Vincent Millay. In her 1918 poem "First Fig," she writes: My candle burns at both ends; It will not last the night; But ah, my foes, and oh, my friends— It gives a lovely light!