Scream Theory
Despite Sidney's refusal to have sex, Billy makes no reference to it when describing his motives. I think that Billy and Stu were lovers. The only reason Billy was Sidney's boyfriend was to get close to and murder her mother, with whom his father had an affair. Sidney and Billy only have sex once, and instead of being sexual (see Sidney's postcoital disenthusiasm), it is Billy's final power play before murdering her.
A second lover could also compensate for Stu allowing his girlfriend to be killed by Billy. Tatum seemed like the perfect match for Stu, and his lack of motive implies that Billy had bullied him into it. Despite this, Stu acts affectionately towards Billy, constantly touching him, throwing him odd glances or banter rife with sexual tension.
TBC
A second lover could also compensate for Stu allowing his girlfriend to be killed by Billy. Tatum seemed like the perfect match for Stu, and his lack of motive implies that Billy had bullied him into it. Despite this, Stu acts affectionately towards Billy, constantly touching him, throwing him odd glances or banter rife with sexual tension.
TBC