"I came to the conclusion that I would love only myself and fight for only myself. If all other people exist to magnify that love, then there is no more a splendid universe than this one... My existence will not vanish."
Users become stronger, faster, more durable, etc. by bonds of loneliness of oneself and others or by being in the recepticle range of their better selves, possibly unlocking abilities related to the affinity and enhancing the existing powers. Some users may be able draw sustenance from the bonds or even slow or stop aging.
Yuichi Hirose (Alive: The Final Evolution) abandoned all human companionship in order to take in the Heart of Acro, greatly enhancing his strength.
Sōsuke Aizen (Bleach) was more powerful than most others, thus leading to loneliness that gave him the resolve to bond with the Hōgyoku to realize his deepest desires.
Kōga Kuchiki (Bleach) suffered a mental breakdown after being framed by those jealous of his power, and believes that he does not need anyone else, that he alone will be the strongest in existence.
Ōko Yushima (Bleach) despises concepts of being with others, believing it to be a form of weakness and insult, and takes great pride of his own solitude and independence.
Papillon (Buso Renkin) was forsaken by his family when he was terminally ill, thus strengthening his resolve to live, allowing him to become an incomplete homunculus and massacre his entire family single-handed.
Despair (DC Comics) gains powers from all forms of hopelessness, and therefore loneliness is part of that source for her.
Zeref Dragneel (Fairy Tail) can only control his "Ankhseram Black Magic" if he loses his regard for life, thus becoming stronger at being alone.
Kamui (Gintama) came to believe that he had to completely empty himself to gain the title of the strongest, which resulted in him leaving his family.
Lord Voldemort (Harry Potter) prefers to operate alone whenever possible, allowing him secretive and successful plans. He passed on this trait to his daughter Delphini.
Masato (Mermaid Saga) suffered 800 years of solitude due to his immortality, thus leading him able to perform tremendously callous acts of feeding the risky mermaid flesh to many women, and overpowering the physically bigger Yuta.
Gaara (Naruto) believes his solitude will magnify his own desire to live, in which he would gain strength in order to protect his valuable existence.
Sasori (Naruto) grew up without knowing parental love, thus his loneliness led to his complete focus on the Puppet Technique, showcased by his genius design and usage, but dark and morbid creation of the Human Puppets.
Representing the loneliness of the Uchiha Clan, Indra Ōtsutsuki (Naruto) was proud and independent due to recognizing his own talent and believing power alone is the key to peace, walking the path of hatred alone.
The second-to-last incarnation of Indra and broken after losing his brother, Madara Uchiha (Naruto) would also gain the same belief in solitude is the key to peace,
...,which thus led him to willingly use and even kill his own clansmen and descendants.
Sasuke Uchiha (Naruto) is the last and current reincarnation of Indra, who came to believe he alone can and will shoulder the hatred of the entire world,...
...even willing to sacrifice comrades and friends.
Sir Crocodile (One Piece) made it clear he never trusted anyone but himself, thus strengthening his willingness to sacrifice even his own organization for his agenda, and expect Nico Robin's betrayal.