I like Henry Dundas (Viscount Melville), and believe him to be one of the only people in Pitt's life that could have filled the role of a father figure for Pitt. In a public and private sense, Dundas had a dramatic impact on Pitt. William respected Dundas's opinions, with good reason as Dundas was quite a clever politician, however quite a few of Pitt's friends, including the abolitionist William Wilberforce, lamented Dundas's hold on Pitt. Pitt drank far too much in Dundas's company, and increasingly this became such a regular habit that it quite possibly instigated Pitt's increasing dependence on alcohol to function. Pitt relied on Dundas; he was, as it were, Pitt's right-hand man and political fixer. Pitt came to depend on Dundas, and when Dundas threatened to leave office on several occasions, Pitt practically begged him to remain in government with him. Dundas also provided Pitt with a place to stay at his villa - Warren House, now called Cannizaro House (Hotel) - in Wimbledon. When Pitt wasn't at Downing Street or Holwood, he could most probably be found with Dundas in Wimbledon. I've seen numerous turnpike expenses showing Pitt's journeys between London and Wimbledon to see Dundas. They were, without a doubt, close. They shared morning rides on horseback, and evening walks at Wimbledon, mixing political business with the easy informality which suited their friendship. There was no clearly defined separation for them between politics and the convivial hours spent dining and drinking to excess.
For the purposes of comparison, I'm presenting two sides of the role Dundas played in Pitt's life. Firstly, for what it's worth, here is what the diarist Nathaniel Wraxall (or 'Rascal', if you're the Duke of Wellington), had to say about Dundas's control over Pitt:
"As early as the year 1787, Dundas attained a commanding influence which no other individual ever acquired over Pitt's mind. With the members of the Cabinet Pitt maintained only a political union: Dundas was his companion with whom he passed, not merely his convivial hours, but to whom he confided his cares and embarrassments...Dundas guided Pitt on many points, and influenced him upon almost every measure; but he effected it by never dictating upon any matter. When discussing public business, he [Dundas] commonly affected to embrace the contrary to the opinion which he knew or believed Pitt to have formed upon the subject. After contesting the chancellor of the exchequer's arguments, Dundas usually concluded by adopting his sentiments, as if from real conviction. This ingenious species of flattery proved irresistible under the control of judgement..." (p. 318)
On the other side of the coin, however, was Lady Hester Stanhope's (Pitt's niece) opinion of Wraxall's testimony. Her physician Dr. Meryon read the passage I have quoted above where Wraxall asserts Dundas's dominance, and this was her response:
"She [Lady Hester Stanhope] denied that Mr. Dundas had any direct influence over Mr. Pitt, as Wraxall avers. Her words were, "Because Mr. Dundas was a man of sense, and Mr. Pitt approved of his ideas on many subjects, it does not follow, therefore, that he was influenced by him"" (Lady Hester Stanhope, in Meryon: 71).
Taken as a whole, perhaps Dundas and Pitt were very similar men who essentially depended, in their own different ways, upon each other?
Meryon, C.L. (1845) 'Memoirs of Lady Hester Stanhope, as related by herself in conversations with her physician, Vol. 2.' London: Henry Colburn, p. 71.
Wraxall, Sir N.W. (1836) 'Posthumous memoirs of his own time, Vol. 2,' London: Samuel Bentley, p. 318.