Assuming this is limited to TTRPGs, then in my mind rules "heaviness" relates primarily to how quickly can I learn the game as a player, how quickly I can master the game as a player, how much I benefit from that mastery, and how much I need the rules to run the game as a GM. It's entirely related to how much work I need to put into learning the game, and how much I need the rulebook during play.
I can think of a few overall factors:
Quantity of systems or mechanics or "phases". If every aspect of play has a different prescribed rules procedure that dictates the order or sequence of play, I'd call that more rules heavy. 5e is somewhat medium here, albeit unevenly. It has distinct character build/creation, exploration (i.e., skills), combat, rest, and roleplaying phases of play. The social and roleplaying aspect, however, essentially has no rules so I hesitate to call it a system or mechanic. This also includes how important the game thinks those systems are. A system that makes it clear that following the rules is essential is heavier. A system that has a lot of different, narrow scoped mechanics with distinctions is also heavier. The distinction between attack rolls, saving throws, and ability checks is additional rules weight that isn't necessarily beneficial. 3e included additional damage systems, monster progression systems, magic item creation systems, etc.
Related to the above is the sheer completeness of the rules. This is related not to how many systems there are, but specifically it's how often the game gives you mechanics that you're supposed to use. Most RPGs at some point kind of shrug and say, "I dunno, it works like the real world so just have the referee make it up." If the game says, "No, no, here's how you do this thing." that's more rules weight even if it's the same system reused over and over. The more the books intrude and dictate play, the heavier the weight of rules.
On the flip side of completeness is intuitiveness or reuse & portability of learned mechanics. This is more of a way to get a discount on the heaviness of multiple systems. For example 5e reuses the same mechanics for skills, attacks, initiative, and saving throws. Roll d20, add attribute and proficiency bonus, compare to a target number. Compare that to AD&D where all those systems were basically unrelated even when they use the d20. 5e, on the other hand, is fairly intuitive. Indeed, without this fact the game it would be vastly more rules heavy than any 20th century D&D.
Complexity of mechanics in actual play. Complexity is not the same as weight, but they're not totally orthogonal to each other, either. AD&D is the poster child of a game with optional, very complex mechanics -- with the infamous
ADDICT PDF probably best exemplifying how complex it can get (excepting that basically has very little to do with how it's usually played). Still, a chart that you must reference during play is a lot of rules weight because it can't really be replicated. You just need the chart. Meanwhile a bonus to a die roll is much less weighty. However, complexity can also just include the number potentially viable of choices you have to pick from and the amount of information you need to keep in your head
if all of those things are defined by the rules.
Game complexity is a deep topic on it's own, though. 5e D&D is hard to judge here because some classes like Champion Fighter have virtually no choices, while others like Druid can require you to pick the correct action from a list of seemingly equivalent mechanical choices, plus know enemy attributes, and plus know spell details. And still others like fairly complex creation rules (primarily thanks to attribute assignment, race, class, subclass, multiclass, spells, and ASI/feats, etc.). You
could just pick a Champion Fighter with sword and shield and not have to think ever again, but you're kind of punished for ignoring the character creation phase of play in 5e. You're really not in AD&D. A la carte multiclassing probably adds more complexity and rules heaviness for the amount of page space it takes up than anything else in the game. In general, however, I think the game rewards and focuses much more on characters with a lot of choice, so I'd put this on the medium-heavy end for 5e. The game generally rewards "solving problems from the character sheet," too.
Quantity of content. A simple game with vast quantities of content that are useful or important to know adds it's own a barrier to mastery, and therefore adds weight. 4e, for example, was a relatively uniform system, and quite simple if you only had to learn 10 different powers. However, the game added more and more content. More feats, powers, items, etc. spiraling into just a huge amount of information to learn and retain. You don't
need that additional content, but, boy, did you ever benefit from it! It's not necessary to play the game, but it certainly is to master it. This means that the release of Tasha's in particular makes 5e more rules heavy just by existing. (It also makes it more complex due to more decisions to make.)
Overall I'd put 5e D&D at:
Character creation & build: 7-8
Combat: 5-7
Exploration: 4-5
Social: 2-3
Overall I'd say 6-7.
1e AD&D looks worse than 5e D&D, but that's only because it's so arcane and unintuitive. In reality you have very few choices out of the rule books that really matter. Mastery of AD&D isn't particularly difficult, either: Be a fighter type or a magic-user and multiclass, multiclass, multiclass. AD&D is actually much lighter as far as rules, it's just that the rules that exist are obtuse. It's just much, much worse at design and presentation, and the overwhelming majority of systems in AD&D
just never get used. The weight is largely empty.