This is largely taken from Robert Harvey's The War of Wars.

Pitt the Younger was descended from two of the greatest political dynasties of the age. His father was a towering intellect, a great orator and a natural leader, William Pitt the Elder, Earl of Chatham. At the time of the younger Pitt’s birth he was the leader of the House of Commons and latter appointed as the Prime Minister of Great Britain.

William’s mother, Hester, was from an equally distinguished family, the Grenvilles, a methodical, highly cultivated family which boasted George Grenville, the Prime Minister who first tried to introduce disinterested administration into corrupt British government and to set Britain’s finances on a sound footing.

The boy was brought up by tutors at home, his prodigious intellect and gifts cultivated with the specific aim of rising to the highest position in the land. He went to Cambridge at an absurdly young age of fourteen, he made his first speech to the House of Commons at twenty-one , he was appointed chancellor of the exchequer by the earl of Shelburne at the age of twenty-three and was made Prime Minister the following year.

The key to Pitt’s appointment at such an early age was not only his brilliance and his heritage but also the support of the King, George III. He had come to the throne seeking to establish the Crown’s power as the lynch-pin of the political system in a country which since the arrival of the absentee German-speaking Hanoverians had been a republic in all but name. He had tried to rule from behind a loyal Prime Minister and after several attempts he had secured one. Lord North, a brilliant man at reconciling the demands of king and parliament for twelve years, but after the American War of Independence he had fallen. So Pitt had been brought in as the King’s puppet allying the royal party and country squirearchy in the commons with his famous last name and his father’s remaining supporters.

I'm afraid I can't really answer the second part of your question. Maybe someone more knowledgeable will drop by. Harvey only mentions that upon Pitt's appointment as the Prime Minister he was greeted by universal derision and leaves it at that.