In the Core rulebook, it states that Dwarves find Elves too frail, flighty and pretty to be deserving of respect. It also states that they have the closest bond with Humans for their industrialist nature and hearty appetites. Where would a Half Elf land in their eyes?
In my games I've always had dwarves treat half-elves with a kind of guarded curiosity. They're human enough to warrant some respect but elven enough to be disdainful. Half-elves always tread lightly around dwarves. Overall the dwarves I feel are on the cusp of hating everyone, regardless of race. They're equal-opportunity bigots that way.
In my games, dwarves treat elves and half elves equally, in the same way real world bigots treat any "half breeds", perhaps even more distrustful than their treatment of elves.