const might also involve some optimizations, e.g. in multi-threaded context.
Let's imagine a value being passed to a function by const reference. This
function starts 2 or more threads and passes the value to them as reference
to a const object as well. What happens in this context? As long it is not
volatile it might be cached in a register, but I think that if the value is
const, compiler has stronger assumption, that this value is good enough to
be cached for all threads...
 

If you have a reference to const, the compiler cannot make
any assumptions about whether it is modified or not, because
of const_cast.  Objects declared const are another matter,
because it is undefined behavior to modify them.