As a result of his viral injection, Wesker was granted a number of superhuman abilities, essentially becoming Umbrella's most powerful Tyrant. Wesker demonstrated incredible speed, reflexes, agility and strength, and it is very possible that he took great pleasure in showing off his power to intimidate his foes. These attributes gave him a number of advanced combat capabilities. Notable achievements of his heightened physical abilities included being capable of dodging bullets at practically point blank range with minimal effort (including rapidfire or multiple shot weapons), being able to cover great distances in short time, performing short dashes of speed faster than the normal human brain could process (causing him to appear to be teleporting), and being able to jump great heights.
Notable achievements of his increased strength included being able to lift large missiles with one hand and throwing them, lifting large steel girders off his body, lifting an adult human off the ground with one hand effortlessly, thrusting straight through the chest of a person with his fingertips, killing a chimera B.O.W. with just one kick, and sending someone flying with a single backhand swipe. The injection also gave Wesker a low-level rapid healing factor which, coupled with his incredible endurance, rendered him nearly invincible to conventional damage. A rocket exploding right in his hands was only sufficient to weaken him for a moment, and thousands of pounds of steel falling a few stories on top of him failed to even incapacitate him, merely dazing him for a few brief seconds, and despite having his face hideously burned at close range, he quickly healed up.
With these powers, Wesker mainly did not require weaponry other than his brute strength during combat, combined with a sufficient strategy and some meticulous observation. Even though he is skilled at martial arts, he did keep his handgun holstered at all times, and was known to never let his guard down, even outside the battlefield.