So I have this Tamron 28-300 (which is 18-200 on a FX body, right?
Sorry if I get that backwards) which is a fine enough lens, but it
goes from f3.5 - f6.3. It's not a huge lens by any stretch.

What I am wonder is why such a lens can't be made that is either 2.8
straight through or has an at least lower f-stop throughout (say 2.8
- 4).

I have the Nikon coffee thermos (i.e. their 70-200/2.8 lens) which in
comparison is huge, so I am assuming that size of the lens is a factor.

My reasoning goes something like the size of the lens is needed for
the f-stop to be so low at higher zoom distance, but the bigger the
lens, the higher the lowest zoom becomes (which is why it's 70-200 and
not 18-200).

Could anyone shed some light on this?

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Sandman[.net]