The reason is not only the extra weight, it's about weight distribution. If you want to understand this the cheap way, buy a 1kg bag of sugar. With one hand, hold it to your chest and see how long it is before you get tired. After a short recovery break, repeat the experiment but hold the bag of sugar with your arm fully extended in front of you, now see how long you can hold the bag of sugar. Until you experience a heavy lens, it's hard to believe the difference even a slightly longer and heavier lens can make. Being able to hand hold a 300mm lens all day changes significantly how and when you'll put it in your kit bag.
I show an example below as one of the bikes speeds toward me. The first picture in the series is amazing, and even the 100% crop (seen below) shows that the focus is absolutely nailed. But as the bike moves closer and the camera runs, the next picture looks okay in full but at 100% is really quite soft as the focus appears unable to keep up with the advancing biker. This is undoubtedly a tough test as the bike is both close and moving in the plane toward me, not across the plane of vision.
The Sigma 300mm f2.8 prime is an older lens that pre-dates Sigma's new range including the Sport (range) lens 120-300mm f2.8 which retails at a similarly substantial £2,799. The lens enjoys variable settings allowing a trade off between focus speed and focus accuracy. I have no experience with this lens so can't comment above other reviews that I've seen suggesting focus speed still lags the own brand lenses. I would suggest however that the Nikon primes deliver both focus speed and accuracy. In addition for the new Sigma, at 3.4kg, this lens undoubtedly falls prey to hand holding considerations earlier mentioned.
Verdict: following a full day at Motocross, I came away with so many great shots that most will never see the light of day. Admittedly however, when keeping my thumb pressed to the shutter release button, focus acquisition lagged in my view. If I were asked to shoot the Olympics with this lens for the cover of Sports illustrated, I might be bothered by this; since that's unlikely and my own Sigma cost less than 75% of Nikon's new offering, I sleep very well at night. Only you know what's important to you but having avoided third party lenses initially after committing to full frame, given the money I saved, I now get it. Would I recommend to a friend? I would point to this review, and then answer yes.