While in MMA training, people have to rotate partners, and the weight, sizes, and genders are all going to be different. During training is where you learn to deal with bigger opponents. It's actually encouraged in order to motivate you to become more skilled.
It's well known that weight and reach makes a big difference in outcomes of fights of all kinds, including MMA. The UFC and other MMA venues originally had no weight classes, and it wasn't so much because it was trying to be "pure". It was mostly because there weren't enough competitors to have weight classes. As the number of competitors increased, weight classes emerged. And the weight classes themselves can change over time because of increased competition.
But that really doesn't change how MMA is trained. You'll still need to train with partners of all different body types.
A question one might have is: Would MMA's techniques or strategies no longer work if the opponent was much larger?
The answer is NO. MMA techniques and strategies aren't optimized just to fight people of the same weight class. They have to work no matter what.
Instead, if you want to win against a much larger opponent, you're going to have to be much more skilled than your opponent is. That general rule holds for fighting in general, not just MMA.
MMA doesn't have rank, so I'll use BJJ as an example. A 100 pound woman who's a black belt in BJJ will have difficulty fighting a 250 pound muscle-bound man who's a white belt in BJJ. She may even lose. She needs to be much more skilled than he is in order to win. Her techniques won't change. Her strategies won't change. But she needs to have trained so much that her movements are smooth, fast, and correct. She gets that over time by continuously pressure testing her skills against larger opponents. And that's something that's encouraged in BJJ training.
There are other topics to consider when discussing weight classes. By reducing the amount of weight between weight classes, it can make it easier for fighters of one weight class go down or up a weight class. And almost invariably, fighters will weigh one or two weight classes higher during training. They have to lose a lot of water weight and fat to cut weight for the weigh-in. Some cut too much and end up hurting their performance on the day of the fight. Those that don't do this cutting and just fight at their natural weight will end up fighting someone who's naturally much heavier. These issues can greatly effect outcomes of fights.
Hope that helps.