Size hierachy for uniform circuits There is the size hierarchy theorem for non-uniform circuits.


  Do we have any size hierarchy theorem for any kind of uniform circuits ?


(By uniform here, I mean DLOGTIME uniform. But I don't know if this matters.)

For example, do $O(n)$-size constant depth threshold circuits have less power than the ones with size $O(n^{10})$ or even super-polynomial ?
Regarding your last question: The paper Size-Depth Trade-offs for Threshold Circuits shows that the parity function requires depth-$d$ threshold circuits with $\ge n^{1+\epsilon(d)}$ wires, which is tight up to the function $\epsilon$.  But for gates not even $\Omega(n)$ lower bounds are known.