So despite the common perception in the TES community that the disappearance of the Dwemer remains a mystery, it is actually quite well known by lore forum regulars what happened to them.
Michael Kirkbride, the guy who wrote most of the stuff about the Dwemer, has repeatedly confirmed the theory. If you guys are interested in reading his comments and a full explanation of what happened, I can link them.
Short version: The Dwemer were trying to escape the sub-gradience system. Basically, in TES, every thing moves down a chain. Mortals are actually just subgradiated et'ada (original spirits) who died during the creation of Nirn. The true reason Lorkhan made Nirn, was to allow mortals to escape what he saw as the "enslavement" of this system. The universe of TES is actually comprised of the dreams of what we call the godhead.
When a mortal sees this godhead, they realize that they are in-fact, not individuals. Most people who see the Tower (the true shape of the universe), zero-sum. In other words, they cease to exist and have never existed. Those who manage to maintain their individuality attain CHIM, or become ruling kings. Essentially, they see the Tower (recognize that everything is part of the same thing) and yet still manage to say "I am."
This gives them pretty immense power. Basically, they are lucid dreamers. They are able to manipulate the dream. Individuals known to have CHIM are Vivec and Talos. Some speculate that others have it as well, such as certain player character heroes.
However, there is a step beyond CHIM. Its called Amaranth. This is when an individual moves beyond the Universe and becomes their own Universe. They enter a state of sensory deprivation and begin dreaming their own dream. These dreams then come alive.
Michel Kirkbirde told us that only one being/thing has achieved this so far. Head over to the official lore forums and find the "Hunt the Amaranth" threads to learn more about this. We still don't know for sure who is the Hidden Amaranth.
The reason this all matters for the Dwemer is that they were trying to break out of the subgradience system. People disagree about whether they were trying to move UP the chain (back to Aetherius and godhood, like the Altmer want to) or DOWN the chain (towards CHIM and Amaranth, like the Dunmer and Men want to.) Either way, their method was Numidium.
They constructed the brass god either as a vehicle or a conduit for their ascension. The metal of the Brass God was actually created using Dwemer souls. When the Tonal Architect used the tools on the heart, the Dwemer disappeared.
People disagree about whether they zero-summed (ceased to exist) or succeeded in ascending. Michael Kirbride strongly suggests (IMO) that they are still bound to Numidium. In a sense, Numidium (the artificial god) could be a reconstructed et'ada. The Dwemer souls may have combined back into something higher up the subgradience chain, a Dwemer oversoul.
The only surviving Dwemer, Yagrum-Bagarn, didn't get combined as well because he was in Aetherius (the outermost realm.) Aetherius is the origin point of the et'ada. Yagrum was, in a sense, already up the chain. Hence he didn't come along. He's unable to have Dwemer kids though for two reasons: he has corpus disease AND in TES the race of offspring is determined by the mother.
In other words, Tonal would have to have a very good reason for being Dwemer. If females in his ancestry are Dwemer, so would he be. But then he would have joined the rest of them. Unless he was in Aetherius at the time of ascension as well. Or if his ancestors were.
It would be a huge revelation though because Yagrum-Bagarn is supposed to be the last Dwemer. Maybe MK himself will comment (we can hope.)


Personally, I think Nord ancestry is more likely. Doesn't mean he can't still revere Dwemer and think he is one. Perhaps MK might say otherwise or another lorumite will have a compelling reason. for why it makes sense.