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.
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).
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.
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.