
Max M. answered 08/23/19
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I love these kinds of connections, and they can be incredibly useful for understanding older, denser, more complicated works. Plus, patterns are fun!
And I would say you should never worry about "reading too much" into something, especially not literature! What I would suggest instead is, on the contrary, keep going! So far you've said, essentially, "outcast scavengers scheming for personal profit." It's a good start, but if you're looking for meaningful connections, dig deeper. If you were going to write a compare / contrast essay, what would you want to talk about? How do Gollum and the Thernardiers see themselves? How do they see the world? What do we know of their pasts and how they got this way? How do other characters see them? What do they want out of life? How, if at all, do they change over the course of the narratives? It's in questions like that that you'll get to the good stuff.
As for the concrete question, Tolkien was notoriously cagey about the allegorical nature of LoTR, so you're unlikely to find anyone who can say definitively what homages he consciously made. Personally, I see some Caliban in Gollum (monsters with a soul, unwilling servants, fighting a metaphysical war with their identities), and since Tolkien was so into ancient mythology, I also see a fair bit of Loki (honey-tongued but vicious, life-saving companions / self-serving connivers, undisguised loathing for the hero's protector (Heimdall and Sam, respectively), ability to navigate both the heroes' and villains' worlds). But I don't know (or really care) how intentionally Tolkien mapped those guys onto Gollum; it helps *me* understand those characters and those books, and if I were to write an essay about it, it would be because I think it might help someone else understand them too.
Anyway, keep asking questions of what you read, and keep pushing yourself beyond circumstantial similarities and start investigating the characters' blood and guts (or hearts and souls if blood and guts are too icky).