I actually think Kate really likes Spencer now; she may have homed in on him originally because she wanted to ally with the alpha-male character in the house, but she seems to have falllen for him quite seriously. Of course, it might just be the clostraphobic, non-reality of the house setting in and highlighting emotions - plenty of evidence for this all round of course !!! ... She'll probably 'make friends' with Sophie, to neutralise the potential of her being a threat, until she is sure of Spencer. But as has been pointed out in this thread, Spencer is one to keep his cards close to his chest. He is keeping kate in suspense ... may be he is playing the game, seeing that she is going to be seen as the 'fittest' bird by the public. He might have to re-adjust this strategy maybe.
However, when he moved into the yard, he did tackle Alex on kate's behalf - his first real direct 'confrontation' in the house with Alex I think. And only because he was protecting KATE's interests. So far, It is being assumed that he will like Sophie and vice versa, purely because of looks match-up. She is also older than him, remember.
Stiull ... Should be interesting ...