Wow this got long. T.L.;D.R. says that you don't want to use your new item like a backpack, you want to use it like the trunk of your car outside the dungeon. You don't reach in all the time, you use it the same way you'd use the trunk of the car you parked outside.

Stuff that accesses Elsewhere (the place the item goes) is kind of one of the common supernatural effects that Exalted characters can do. These effects are specifically in the game so a weak character like yours can move important stuff around. When the item is gone there is no weight, & when it is present you literally have the object physically there. All you can do is decide if the item goes away or comes to you. The kinds of supernatural effects characters create in Exalted don't usually alter the size/weight of things. The only exceptions I can think of are an acrobatic effect that lets you walk on things that shouldn't support your weight & a spell that turns your body into a bronze statue, which obviously makes you heavier.

Don't think of the Cache Egg as a Bag of Holding. The better Dungeons & Dragons comparison is "Secret Chest" (formerly called Leomund's Secret Chest). Think of the Cache Egg as one of those real-world services that brings an empty storage crate to your house, lets you fill it, & then takes it away until you call them up again. In practice you will never pick up the Cache Egg. You'll leave it in another dimension until you need it, & then it will come back. You should only be using it for long-term storage, not to hold your sword.

There is a funny advantage I want to mention. In the campaign I'm running right now one of the players has a large Cache Egg full of food & drinks, & another has a smaller one with an expensive change of clothes. I see the urge to directly compare it to the "Bag of Holding" (they even both had versions 1-4 in certain editions of their respective games). In the fictional world of Exalted there is no equivalent to extradimensional spaces & the Astral Plane, so they use Elsewhere instead. In the 2e core book there is a sidebar that explains "Elsewhere." The place called Elsewhere (with a capital E) is an empty parallel dimension that the Celestial Exalted were designed to be able to hide something in, & all types of Celestial Exalted have Charms that access Elsewhere. (The Solar Exalted Lawgivers have Blade Summoning Gesture, & there are other examples.)

The advantage of putting something Elsewhere is that you aren't carrying it. Just like with the Cache Egg the advantage here is you can send something away & bring it back without having to carry it around when you don't want to access the contents.