Also, it is easily imaginable that some creatures might trigger one of the two limits (height or weight) but not the other. For example, a bonecrusher skeleton (a ogre/savage minotaur skeleton) might easily be Large, in reference to reach, size occupied, and height) but weigh a lot less than another Medium creature (say a Gargoyle or other stone creature).
In general, however, I think that the best signifier of Large size is "size of occupied squares". A minotaur or goliath, while large relative to many other races, doesn't really "occupy" four squares. A tentacled beastie, even though it might mass just as much as the Goliath, might sprawl out over 4 squares quite easily (and still be shorter than the Goliath, too).
Like many things in D&D, Large has a specific game meaning that doesn't perfectly map onto it's real world usage. Plus, that game meaning has a specific boundary that will seem arbitrary when the real world has graduations of meaning. A creature either fits into one square, or four (or two, perhaps). There are no creatures which occupy 30 square feet, or 50 square feet, or 75 square feet. There's 25 square feet (Medium) and 100 square feet (Large). Sometimes, things "really" would be a lot more of an "edge case".