The weight of a rules system should take in more factors than just "do you have to look up tables!"
You have to take into consideration what goes into reading, understanding, and memorizing the rules. For example, in D&D 3e/4e there's an entire nomenclature built around miniature movement. You have to know about actions. Move, Minor, Swift, Standard, Extra, etc. You have to know what a push, pull, and slide are and what the differences between them. You have to know what a 5' Step/shift are. You have to know the various conditions and what they mean. You need to know what type bonuses are and when they stack. And so on and so forth. For Fate Core, you have to know about boosts, zones, compels, declarations, contests vs. conflicts, invoking, refresh, etc.
Then there is how complex something is in play. Even Fate Core gets complex here with a slew of aspects being created, invoked, disappearing, and reappearing as the game is played out. Have you used your free invoke yet? Is that boost used up? Is that aspect still in play or did we negate that? It isn't overly complex, but it is something to keep track of and that increases, in my opinion, the weight of the game. No, I'm not having to look anything up in the books, but I'm having to keep records on minutiae in order to properly run the game. Contrast that with something like Dread where there is only one mechanic: pull from the tower and succeed or die. The Window, in contrast, might play out an entire combat in a single roll. BAM! You're done. Move on to other stuff.
Lastly, there's prep time. How much time am I spending to get ready for the game. A half page of hastily scribbled notes gets me a session of Dungeon World. Contrast that with my epic Planescape 3e campaign in which I'd spend hours carefully crafting antagonists and had a binder of absolutely amazing adventures. One isn't better than the other, but there's definitely a difference in weight here.
And, there are games in between and even further out from each end.
So for DDN, I'd say the game is probably going to be on the heavy side, from what I've read in the playtests. Even the basic rules look like they're going to cover a wide array of rules. There may not be miniature combat in the base, but there still seems to be a lot of stuff in there. You've got to read up on your racial rules, your class rules, combat rules, what's a feat, what's alignment, what's a proficiency, attack rolls, advantage/disadvantage, ability score vs. ability modifier, damage types, spell rules, etc. These are all things that are taken for granted by most current D&D players, but these are rules that can be considered significant compared to what I would classify as rules-medium games (like FATE Core).
Gameplay-wise, I have to admit its been a few play packets since I actually played a game. Maybe the 2nd released playtest, actually... I think complexity has gone up since then, but I can't really speak from experience. From playing, I didn't think gameplay complexity was very high. I didn't have much to track, and I didn't have a lot of tactical or strategic decisions to make. I might have classified this as light.
Prep I can't speak for, as I didn't run the game. So, I can't speak from experience on this matter.
Overall, I'd say DDN is just on the rules-heavy side.