Why does the thickness of a wire affect resistance? For small thicknesses of wire, it's pretty obvious why resistance affects thickness. (The electronics squeeze to get through). But after a certain thickness shouldn't the thickness become irrelevant?
For example if your trying to pour a bucket of water through a straw, the thickness of the straw is obviously gonna be a bottle neck- the bigger the straw, the easier it is for water to get through.
But if you try to pour a bucket of water through a tunnel - the size of the tunnel doesn't really matter, because the tunnel is already big.
So after a certain thickness shouldn't the thickness stop mattering?
 A: All (non-superconductor) metals have electrical resistance, no matter how thick a wire made of them is, as the conducting electrons are always "bumping into" the atoms in the lattice of the metal, slowing them down.  Therefore there is always a resistance that can be reduced by increasing the cross sectional area of the wire (by allowing more free electrons per unit of area).
By contrast once a pipe carrying water becomes of a greater diameter than the body of water flowing through it, there is no resistance that can be reduced by increasing the diameter of the pipe, and thus the analogy between water and electricity fails at that point.
(imagining the water pipe to be filled with saturated sponge makes the analogy closer to the free electrons slowly migrating in a metal)
A: GOOD question and thinking
But the thickness still effective whatever the value is

If thickness value is big and battery has limited charges it will be discharged for example in one second
If thickness is very very big for example 1000 times than before the battery will be discharged in one millisecond 

that's it!
