Thermal equilibrium + heavier mass

Why is it that the object with the heavier mass influences the final temperature (once the two objects in contact have achieved thermal equilibrium)?

For ex. a copper block (4 kg) at 0 degrees and an aluminum block (1 kg) at 100 degrees.......in this case, the final temp ends up lower (36 ish degrees), I'm guessing because the copper (heavier block) was colder, so it influenced the final temp. But is there a deeper reason besides the fact that its heavier? (In this case, you cant say specific heat capacity right? since Al has the higher capacity)

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It is precisely because of heat capacity. Which specific is J/kg/K and heat capacity is J/K

So although Al has the specific capicity, the object has a lower total heat capacity (not sure on the nomenclature here) becuase there is less of it.

If there were only 2kg of copper the Al block would have a higher total heat capacity.

The difference is becuase becase specific heat is an intensive property and heat capacity is extensive.