I also think the length of “the teach” in an important aspect. I’ve played games where it took an hour to set everything up and learn enough to get started. That definitely requires a special level of focus and investment on the part of the players.
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IMO two different things can make a game heavy, and having either is enough even if you don't have both.
First, is complication of decisions. This is the classic "heavy" angle, how much thinking you have to do each turn to execute your strategy.
Second, is the actual meta aspects, such as rules, or pieces, or setup. A game that is literally heavy by weight is highly likely to be heavy, especially if combined with lots of rules or pieces or exceptions. Even if the turn-to-turn is relatively simple, the act of setting everything up and having to learn & remember a whole slew of rules can make a game heavy
At first I was going to say how long it takes to play.
Not to say all short games are light, but longer play time usually translates to complex gameplay - how much consideration is requires before a player makes a move?
But then again plenty of shorter games still feel quite substantial and "heavy" too, though.
Gameplay complexity would be the main thing I guess. Maybe its how many choices does a player have at each turn? How many ways are there to achieve a win?
Too complicated to learn whilst drinking?