The idea that the 750 GeV anomaly might be a top-antitop bound state has been taken to a new level by Froggatt & Nielsen, who have sketched a whole phenomenology for their particle. The reasoning is "crude" (their word), but still on a much higher plane than any mere numerology of masses.
So things may be about to get serious there. Meanwhile, I want to enumerate a few relationships which are still just numerology, but have the potential to be part of a genuine theoretical synthesis.
mH ~ mt/√2
Hvev ~ 2 mH
m375 ~ 3 mH
m750 ~ 6 mH
mH is the Higgs boson mass, mt is the top quark mass, Hvev is the Higgs field vev. m750 is the mass of the 750 GeV particle. m375 is the mass of a 375 GeV particle that Lubos may have found in the data.
The picture I get is that the Higgs field is a top quark condensate, the 750 is a sort of loose bound state of 6 Higgs bosons (that is a "1S" toponium when analyzed at the level of quarks), and the 375 is like the 750 but with only half of the available top states occupied.