There seems to be something about NM and Becky's money. He stole her cheque (even though he couldn't cash it, he didn't want her to have it), he refused to pay her the £100 that he owed her. He thought his mother might be about to buy her a new tv, which angered him.
He somehow thought that what she had, should be his. He had absolutely no respect for Becky as a person, and she knew it. He treated her both before and after death with utter contempt.
As an older step-brother, he could have taken on the role as big brother/protector, as he had known her since she was a child, but for whatever reason, he chose to do the opposite, and torment her.
He wanted complete control over her, and in the end, he got it.
I think this situation was the culmination or merging of several factors.
I am not educated in psychology so this is my own layman's perspective, probably influenced largely by how I see the world, and therefore capable of being quite incorrect.
I think the pair of them felt great injustice and bitterness about having no stability and control over their early lives. What they had lost as children, in terms of mothering, created this huge fear of further loss, and lack of self-worth. In NM's case this is characterized by his hoarding, filling up his life with material possessions. In SH's case, by her pairing up with such a horrible, loathsome, slimy, disrespectful partner. She needed someone, anyone. He could not operate in a relationship with anyone discerning. A match was made.
I honestly do not know if rape fantasies and rapes are the result of anger and hatred towards women, (mothers?) or an important part of the perpetrator's humanity and compassion just being absent. Both of them, judging by their behaviour after Becky's death, strike me as having psychopathic and sociopathic traits.
I think in relation to Becky, both NM and SH felt extreme jealousy and this would be true whatever happened, barring a rejection by her parents, as had been the case for them. Only that would make them feel equal. Seeing Becky rejected and suffering. Becky receiving love, money, material possessions, gifts etc would make them seethe.
As for the incident, IMO it was a culmination of this hatred and desire to hurt/harm Becky, together with the opportunity to enact their sexual fantasies - controlling and taking from a woman, using her, treating her like a piece of meat. Becky fit the bill, she was their perfect target. It turned NM on, possibly SH (I don't know enough about her sexuality) but if not then she would do this to keep her "love", it satisfied their depraved sense of taking what they were owed and were never given by women in their lives.
The only thing I am glad about is that they were caught before doing this again to anyone else, and that Becky did not give them what they wanted, she gave them a big fight and she got them caught and exposed them.
That is why the motive given makes NO sense, it is utter rubbish, and that is why they will never ever admit to what drove them to do it. They are forever shamed by the fact they were not loved enough by their mothers. It fuelled their hatred and their sick existences.