Dynamaxing/Gigantamax are not physically changing the Pokemon.
Joe Merrick pointed this out on his Twitter; according to Ohmori and Masuda, Dynamaxing are projections. Dynamaxing, along with Gigantamax, are a new gameplay mechanic that will be introduced in Sword and Shield. They allow Pokémon to grow giant during battle.
That means the real Pokemon is somewhere in that projection, completely unchanged.
Because Dynamaxed/Gigantamaxed Pokemon are simple holograms, they have no actual weight. A Dynamaxed Inteleon is certainly taller than a Dynamaxed Pidove, but their height ends up being 119'2". (Although that doesn't seem to be canon.)
All of the Pokemon's base stats except for HP are unchanged.
Dynamaxing provides Pokémon with an increase to its maximum and current HP (with the exception of Shedinja) by the same factor. The amount of HP gained depends on the Pokémon's Dynamax Level, which can be increased with Dynamax Candy. At Dynamax Level 0, a Pokémon will gain 50% more HP. For every Dynamax Level above that, the Pokémon will gain 5% more HP, up to a 100% HP increase at Dynamax Level 10. All other stats, as well as its Ability and held item, remain the same.
Whenever a Pokémon enters into or reverts from Dynamax, its current HP is adjusted to retain the same percentage of HP remaining (rounded up). For instance, if a Pokémon at Dynamax Level 10 has 100/200 HP remaining, then upon Dynamaxing, its HP will be adjusted to 200/400. Conversely, if the same Pokémon has 101/400 HP in Dynamax form, then its HP will be adjusted down to 51/200 when its Dynamax expires.
Max Moves are likely the result of being near a Power Spot (which allows Pokemon to Dynamax/Gigantamax in the first place) and aren't the effect of actually changing a Pokemon's stats. The ability Power Spot (Exclusive to Stonjourner) raises the power of an ally's moves, so it's safe to assume Gamefreak modeled this ability after what really happens at Power Spots.
Eternatus is the Pokemon that allows Dynamaxing/Gigantamaxing to exist in the first place.
Eternatus serves as the source of the Dynamax and Gigantamax phenomena in Galar due to its power leaking out in the form of Galar Particles following its defeat thousands of years ago by Zacian and Zamazenta. Pieces of its body imbued with its power rain down throughout Galar in the form of Wishing Pieces and Wishing Stars.
It is also stated that Eternatus can stop other Pokemon from Dynamaxing in it's presence. Eternatus is sort of the Master of Dynamax.
Eternamax Eternatus' weight is still unknown, but we have a canon height of 328'01".
Eternatus works differently because it's not simply Dynamaxing, it's Eternamaxing. This seems to be a special subset of Dynamaxing only Eternatus is able to access. In this form, it's stats actually change.
Sp. Atk: 145
Sp. Def: 95
Sp. Atk: 125
Sp. Def: 250
Because Eternatus is pretty much the creator and controller of Dynamax, it only makes sense it should get it's own buffed, special form.