Might Makes Right
Most of Fisk's bulk is actually muscle, not fat; his enormous size is comparable to that of a sumo wrestler. Wilson Fisk is learned in several types of hand-to-hand combat, and uses his enormous bulk as a means of defense as much as attack. As such, he is able to fight super powered heroes, like Spider-Man, without fear of being seriously harmed or killed.
His immense size and strength notwithstanding, Wilson Fisk's true power lies within his skull. As a genius planner and strategist, he is able to control vast amounts of dedicated thugs, henchman (like the Arranger, Big Turk, Blackie, and Blinker), assassins (including Bullseye and Elektra), government officials (like Randolph Cherryh), scientists (Dr. Jonathan Ohm/the Spot), specialists (Alistaire Smythe, the Tinkerer), and a general assortment of petty criminals in order to achieve his nefarious ends. Even Super Villains like the Hobgoblin, Sandman, Typhoid Mary, and Mysterio have been known to pledge loyalty to him. Fisk's talent for manipulation has duped powerful and well-connected agencies such as the NYPD, the FBI, and S.H.I.E.L.D.
By donating large sums of money to charitable causes, hiring a crack team of attorneys, and choosing to be as hands-off as possible in his illegal operations, he has built himself a pristine reputation that would prevent the press from ever linking him to any kind of chicanery.
As if he wasn't formidable enough, he is sometimes known to carry a walking stick that can fire a laser pulse powerful enough to disintegrate a normal handgun. It, along with his diamond-studded tie, can also spray a concentrated dose of sleeping gas. Fisk has even utilized a Vita-Drain, which is a machine that transfers life force from one person into another, and a brainwashing machine designed by Dr. Gerhard Winkler.
Rivals
You don't rise to be the leader of Manhattan's criminal underworld without making a few enemies along the way. His earliest adversary is the original "Kingpin," Silvio Manfredi, AKA Silvermane. An immigrant from Italy, Manfredi builds up the criminal organization known as the Maggia in Manhattan. After Manfredi is sent to prison for tax evasion, however, Fisk seizes a good chunk of his territory and power.
Some brazen reporters like the Daily Bugle's Ben Urich try to bring Fisk down by hunting for evidence of his sins, of which there are many. He is warned to stop snooping around by Elektra Natchios, when she works as Kingpin's enforcer. Sadly, when Urich refused, she impales him and leaves him for dead.
Kingpin frequently crosses paths with Spider-Man. To protect himself against the Web-slinger, Kingpin once allies himself with Justin Hammer. By trading construction contracts with him, he is able to utilize the services of Electro, who overpowers and captures Spider-Man when he breaks into Fisk's offices. When Parker is unmasked, luckily, Wilson has no idea who he is. Fisk is bested my Spider-Man, though, when Fisk accuses an associate, Mr. Big, of betrayal. He places Spider-Man's mask on Big's head and crushes his skull. This is caught on surveillance footage, which Peter obtains and sends to Urich. With concrete proof of Fisk's treachery in the hands of the press, the Kingpin is forced to flee to Brazil.