Weight is a game's complexity and difficulty of play, though there's no standard definition.
Weight tends to be classified as light, medium, or heavy. As an example, Bridge would be at the heavy end, while Dominoes would be at the light end.
Greater weight means a game is harder to learn and play, and will appeal to far less people.
Lighter games also tend to have less components. This appeals to more people, given financial and space constraints.
Given two otherwise-identical games, the lighter one is superior.
When developing larger games, each change or problem requires long periods of thought, and there are so many components to update, each revision. It's far less fun than designing a lighter game.
Heavier games are also much harder to design. When a big group of systems just isn't fun, it can be extraordinarily hard to analyse.
Don't design anything above medium-light, until you're onto your 20th design.
At the end of it all, there's no extra reward for designing a heavy game. Likely the opposite is true. Everyone will play a medium-light game. Only a minority of people will play a medium-heavy game.
I regard designing above medium weight to be almost unnecessary. If your game is heavier than medium, I'd be almost certain that it shouldn't be.
Medium is the new heavy.
Medium-light is the new medium.