To begin, I’m primarily referencing an excellent article from 1984: The Apotheosis of George III: Loyalty, Royalty, and the British Nation 1760-1820 (http://www.jstor.org/stable/650761).

The author notes that since the Restoration (late 17th century),

no English or British monarch other than perhaps Anne had achieved more than a partial or transient popularity; no sovereign at all had been able to act as an unquestioned cynosure for national sentiment.

Looking at it through that lens and speaking quite generally, we can appreciate that the status and popularity of monarchs among the citizenry was neither invariable nor entirely positive. Another consideration is the great deal of social unrest that marked the end of the 18th century in Britain including but not limited to “class tension, reform campaigns, and radical or proto-revolutionary protest”.

In this period, however, there was an uptick in middle-class patriotism and, in light of the close succession of conflicts with foreign powers, manifestations of the “the flag-saluting, foreign-hating, peer-respecting side of the plebeian mind”. This, to a degree, was fomented by the integration of Scotland in the 1740s (to be clear, I mean that Scots were actively taking on varieties of British nationalism, as well as cultural and agricultural practices). Overall there was an increasingly positive view of country for several segments of British society, enhanced by victories in the Seven Years War. There was a natural extension of these positive sentiments to the rulers of Britain, and George III no doubt rode this enthusiasm into his reign.

But he really did not outwardly embrace or display this enthusiasm, did not in his presentation of himself embody the lionized British sovereign, until after 1780, and herein is this answer to your question. The loss of the American colonies was the capstone to an interlude of foreign conflict and declining prosperity for Britain which occurred in the mid 18th century, and preceded and accompanied George III’s rise to power. It also precipitated many forms of nationalism I’ve discussed. However, around 1780, after the loss of the colonies, George III, widely viewed as unwaveringly patriotic, a man of British uprightness and fortitude, then more than ever seemed a bulwark against national humiliation. This was followed quickly by George’s victory over the Fox-North Coalition (Wikipedia, just for expanded reading), which timed quite perfectly to seat this fairly newfound identity.

I would argue the George III was a skilled tactician when it came to public relations, and used these events as well as other opportunities and aptitudes (the general dislike for his heir, advocating patriotic national celebration, patronizing the arts, etc.) to increase his stature well beyond what is was in the first two decades of his reign. I hope this is helpful.