Marquez-Pac 4 shows the importance of strength and conditioning

A proper periodised strength and conditioning program can make a big difference as shown by Marquez' obvious increase in punching power for this fight. Pacquiao looked good in terms of his boxing but he was clearly outgunned. Note that Ariza claimed Pac hadn't been following his strength program. People are going to call PED's just like when Pacquiao moved up and started proper conditioning but that's because boxing is 'old school' and full of uneducated opinions.
The old 'punchers are born' line should be thrown away, there's no reason not to embrace modern training methods and boxing coaches need to get that through their thick heads.

 

Technique and balance are the most important things but if all the links of the chain (the muscles and tendons) are stronger and have the correct properties for the movement of a punch then power will be improved. Muscles contract with more force and tendons recoil at greater speeds after periodised strength training.
A tendon is like a rubber band, Your brain tells your muscles to contract and your muscles then perform work on the tendon. If the tendon is loose (compliant) then it takes longer to take up the slack and recoil. What that means is that there is a delay between your brain telling you to do something and you actually doing it. That's called the electromechanical delay.
Heavy weight training makes the tendons stiffer so there is less time between a decision and movement. A stiffer or thicker elastic band also recoils with more force if it's stretched the same distance as a thinner or more compliant tendon.
So your movements are quicker and more forceful, even though lifting a heavy weight slowly isn't sports specific to boxing. Heavy weights also help you to recruit more muscle and prevent inhibition of force from the neuromuscular system.When you're stronger it improves your fine motor movements and skill learning as well as less nervous system resources are needed to perform the movement.
It's important that it's part of a periodised program though, you can't perform heavy weight training right up to the day of a fight. When tendons are stretched you lose energy through heat loss. To make your tendons more efficient and lower hysteresis (heat loss) then plyometric training needs to be incorporated. After heavy weight training plyometrics are more effective as your ceiling is higher for power production. Recovery is very important and less is more when developing strength and power.
The heavier you are the stiffer your tendons tend to be (Women have compliant tendons), transferring the weight through the kinetic chain effectively while maintaining balance makes a big difference as well so that's why the heavier the person the harder they'll tend to punch.
I think it's particularly important for lighter fighters to lift heavy weights, training for strength (not hypertrophy).
If anybody tells you that punchers are born then it's they who should be ridiculed. Most people don't even know that slow twitch fibres can be trained into fast twitch fibres, for a long time people only thought that fast twitch could be converted to slow twitch. Everything is trainable, what you do alters your genetic expression and neuromuscular recruitment capabilities.
Boxing is in the dark ages, you can see in life that when people don't understand something they ascribe it to god/the supernatural/they were born like that and choose tradition (something that isn't challenging or scary). That's a lazy defeatist attitude that's still prevalent in the boxing game. Nothing is just because. /endrant