Why do lone pairs of electrons have a higher repulsive force?
Bonding pairs are stabilized between two atoms. Since there's no atom on the other end of a lone pair, it spreads out more than would be if it were in a bond. Lone pairs therefore repel more because the charge density is spread out more, that is, it's bigger.


  I have read that lone pairs have orbitals which are shorter and more round


This is technically true in the sense that you'd want to have higher $s$ character in a lone pair orbital. But you're comparing possible ways to hybridize orbitals for lone pairs, as opposed to comparing lone pair atomic orbitals with bonding orbitals.