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.
Design space is the number of components you can create within the rules of your game. The more expansive your rules, the more things you can create.
In Chess, the rook moves vertically and horizontally, while the bishop moves diagonally. If you try to invent new chess pieces, you'll find it difficult. All the simple ones are taken, so your new pieces will have to be more complicated. Technically, you could just make infinite new pieces of increasing complexity. The design space of Chess is very limited, and most of it is used.
Almost all games I design are medium-light (half way between medium and light). I can explain the game in a few minutes, and a game tends to last around 30 minutes. Medium-light gives me just enough design space. By fully mining this design space, I can create enough interesting things, though it can sometimes be a squeeze.
Radlands has won praise for being a very elegant and focused game, unencumbered by rules and procedures. However, the design space of this game is very small. The game has 34 camp cards. Why weren't there more? I came up with every camp I could think of, and couldn't think of any more.
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.