A planet is a location, not an object
The rules (DMG, p.246) have this to say about what an object is:
For the purpose of these rules, an object is a discrete, inanimate item like a window, door, sword, book, table, chair, or stone, not a building or a vehicle that is composed of many other objects.
The Earth is composed of all sorts of components. Rocks, trees, buildings, people, tectonic plates, oceans, mantle, core, etc. Same goes for the moon. If your average hut or wagon is not an object, what chance does a planet have?
There is no official ruling, but allowing it does not seem to be unbalanced.
As you mentioned in your question, there are no explicit rules stating how the Net interacts with being Oversized (made for something larger than Medium), and I cannot find any official statements from Sage Advice addressing it. Therefore, this is purely up to the DM.
But, for the sake of looking into this a little more closely...
Prior Edition Precedent
Per the 3.5E SRD:
A net is useful only against creatures within one size category of you.
So, in 3.5E, if you were a Medium creature, then a Net sized for your use would work on Small, Medium, and Large creatures, and nothing else. Therefore, if you were Large and using a net made for a Large creature's use, then it would work on Medium, Large, and Huge creatures. So, per the 3.5E rules, an oversized net (made for a Large creature) would work on a Huge creature.
So, there is established D&D precedent for a Net targeting different sized creatures based on the size wielder it is made for.
Thematic Analysis
While there is no explicit statement saying this, logically it follows that the 3.5E ruling works for this reason: too small of a creature would fit through the gaps of the net and not be restrained, while the net wouldn't be big enough to entangle a creature that was too large (you might wrap it around one leg...but that's not going to accomplish much).
Mechanical Analysis
A weapon that can apply the Restrained status is certainly useful. Restrained is a fairly nasty condition. However, a net is quite easy to get out of...for most creatures, it just eats up an attack or an action, and there are lots of things that do that.
Additionally, if we take a look at Grappling...
The target of your grapple must be no more than one size larger than you and must be within your reach.
So, a Medium Creature cannot grapple a Huge creature, same as they can't hit them with a Net. But an Large Creature can grapple a Huge creature. So, even within 5E, there's precedent for player-applied conditions that only work on certain size creatures scaling with your size.
Conclusion
Based on the 3.5E Precedent, and the way Grappling already behaves, I see no reason why this would be unbalanced, and it makes sense from a thematic perspective. If you are still uncertain and want to add a drawback to this, then adopt the downside provided in 3.5E: As you increase the size of the net, it stops being able to restrain creatures that are too small.
Best Answer
... an object that is neither worn nor carried ...
... prevents you from casting the spell offensively on, say, the battleaxe or armor of the giant you are fighting. If you kill the giant, its battleaxe or armor are now valid targets of the spell (as is the dead giant).
What matters is not if the object can be worn or carried but if it is being worn or carried right now.
The size of the object is not relevant provided that it is a single object - a battleaxe or armor are single objects (probably), a castle or tavern aren't (probably) and a wagon might or might not be. Basically whether a thing is a single object (and a valid target) or a collection of objects (and isn't) is DMs call.