I'm playing a ranger who's using the Guardian archetype. The Guardian form is Large, and I would like to use two warhammers since I have the Ranger's two-weapon fighting style. Would I be allowed to use two warhammers without disadvantage despite their normal weight since my size is Large?
Not without the Dual Wielder feat.
The rules for two-weapon fighting don't change for Large characters.
When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
(PHB, p. 195)
Note that you don't have the option of using non-light weapons at disadvantage; you can't dual-wield non-light weapons at all by default.
The Dual Wielder feat removes this restriction:
You can use two-weapon fighting even when the one-handed melee weapons you are wielding aren’t light.
(PHB, p. 165)
Note that there's no prohibition against using heavy weapons for two-weapon fighting with Dual Wielder, but they do still need to be one-handed or versatile. There currently aren't any heavy, one-handed weapons, however.
Assuming you are following the Guardian Form rules found here, then as far as I can see, this does not grant the ability to use outsized weapons, or any other implied features from gaining Large size (i.e. the creature is not stronger, does not do more damage on attacks etc.)
There is not a general link between having different sized PCs and other mechanics that you might expect to scale (compare with 3.5E and Pathfinder which do include a set of changes to stats, attacks and defences as well as explaining how weapon damage should scale). The changes you get automatically with Large size are taking up more space on the battle field, plus a few rules which use the size value directly to compare with others, such as limitations on who you can push or grapple (and who can push, grapple or maybe swallow or envelop you).
Instead the Guardian Form has a specific set of supernatural abilities, including extended reach, fast healing and Large size. The size here works with the damage recovery and extra reach to create a good combination of defensive abilities. It's a nice set of features for holding a position and controlling the battle close to you. It does not include any implied extra benefits