He seemed a little bit too quick with his dagger, and had shown little reluctance to do something dirty to benefit himself. He had a chip on his shoulder against humans, and had indirectly expressed multiple times that he bore Aslan (and the four Narnian royals) no loyalty, thus may have felt that it was unfair that such a treasure would belong to humans instead of him. In holding this attitude, what would he have not done to obtain what he felt to be his?

On a side note, a lot of folklore that likely inspired Lewis portrayed dwarves as bearing excessive loyalty to gold, such as in The Volsung Saga. You can also see similarities between Tolkien's dwarves, such as Mim, Thorin, etc. and Lewis' black dwarves.

I wouldn't call him a kleptomaniac, just a Black Dwarf.
Black Dwarfs (not dwarves in Narnia) seem to have different ethics from Red Dwarfs, and might be ready to help themselves to treasure that isn't theirs. 
I agree with you, Azog, that it's common in fantasy literature to depict dwarfs (dwarves post-Tolkien) to value gold, jewels etc.

I always interpreted this scene as Trumpkin coveting the gold and wanting to keep Nikabrik away from it! Made me think less of him. I never took a shine to his character partly because of that.

Aside from Prince Caspian I don't think Lewis ever differentiated between the Red and Black dwarves. They were always lumped together as "Dwarves."

@cobalt-jade 

Oh, I'd never thought about Trumpkin desiring the gold! Yes, that's possible. 

Please excuse my mentioning it, but they were lumped together as 'Dwarfs', which is the standard English plural (as used today for members of Dwarfism community).

(Lewis didn't copy Tolkien's variant plural 'dwarves', although over 50 years of copycat fantasy writers seen to have done)

@cobalt-jade There wasn't much suggestion of that. Just because he admired it and was amazed by it didn't seem to indicate that he would take it for himself. Also, Caspian trusted him enough as his regent, which would suggest that wasn't in his character.

Posted by: @cobalt-jade

I always interpreted this scene as Trumpkin coveting the gold and wanting to keep Nikabrik away from it! Made me think less of him. I never took a shine to his character partly because of that.

I'm just wondering where this conclusion is coming from, as it never crossed my mind as a reader and I seriously doubt Lewis intended readers to interpret it that way, based on everything we know about both Trumpkin and Nikabrik.

Perhaps you're going by the fact that we're told "The Dwarf's eyes glistened as he saw the wealth that lay on the shelves"? That could suggest that Trumpkin himself is thinking greedy and acquisitive thoughts, and if that's all we were told, it might be a fair conclusion. But at this stage in the story, we've already seen enough of both Trumpkin and Nikabrik to know how much of a contrast there is between them. Trumpkin is sceptical and distrustful of anything he hasn't seen proof of (like Aslan) — this seems to be a common attitude among Dwarfs in Narnia — but he's basically honest and good-hearted and he doesn't shy away from doing the right thing once he's sure enough of what the right thing to do is. We don't have any evidence from the text that he's governed largely by selfish motives.

Nikabrik on the other hand, right from the moment we first meet him, is portrayed as a far nastier character who doesn't seem to be interested in anything unless it directly benefits him and his own people, regardless of the consequences to anyone else; we see this even more clearly a little further on in the story, when we learn he regards the White Witch as a more likely benefactor than Aslan and is planning to bring her back from the dead. It's very easy to believe that he's also the sort of Dwarf who wouldn't hesitate to plunder the royal treasure chamber of Cair Paravel if he had the chance.

Whereas we never see any evidence that Trumpkin would seriously consider doing something like that, so to me the most logical conclusion is that when he says "It would never do to let Nikabrik see this", he's simply pointing up the contrast that's already been made clear between the two Dwarfs since the first scenes where we see them both in Trufflehunter's cave. Trumpkin presumably does find the treasure impressive (how many earthly beings wouldn't?), which explains why his eyes "glistened", but we know him well enough to know he's not going to be overtaken by lust for it — whereas he's very aware that Nikabrik would be, and wouldn't have any scruples to hold him back.

Aside from Prince Caspian I don't think Lewis ever differentiated between the Red and Black dwarves. They were always lumped together as "Dwarves."

Hmmm, there's also the fact that in The Last Battle, Griffle, the leader of the Dwarfs who turn bad, is a Black Dwarf, whereas Poggin, the only one who breaks away from the group and joins Tirian and his friends as a loyal ally, is a Red Dwarf. So it does seem to be the case, at least in Lewis's characterisation, that the Black Dwarfs are more likely to turn to evil. Of course it's a reference to their hair colour, not their skin colour, but I'm amazed I haven't yet seen any critics pouncing on this as further evidence of racism in the Chronicles... (Just to be clear, I don't think Lewis was intending it that way, but if I were in charge of filming the next screen version of Narnia, I'd make sure we see evidence that Dwarfs of any hair colour can be either good or bad, just so no-one can read anything into it!)