Fridge Logic: It would have been easier for Gregory to stay in London and break into and search the empty house any time after it was abandoned. He was already breaking into Apt 5 next door, so why go through all the trouble to marry Paula?
It could be that he wasn't sure if Paula saw him and could be a potential witness to the murder and attempted robbery. By marrying her and causing her to go insane, he wouldn't have anyone to testify against him, could search for the jewels without any interference or caution, and would undoubtedly inherit the aunt's house and Paula's fortune to boot.
And as the husband of the house's new owner, him finding the jewels is a lot less suspicious. Cameron's superior even says that the jewels were "too famous" to be sold, so there's no way for Gregory to find them and not look suspicious. But if he's living in the house for a while - they've been married for about six months by the climax - then no one would think anything out of the ordinary of him happening to find them in the attic.
Was Elizabeth in on the scheme? When she denied that Brian had been in the house, was she actively helping Gregory, or was she just afraid of getting fired? Likewise, did she deny the sounds in the attic because she was covering for Gregory, or because she was hard of hearing?
I just got back from seeing the movie and she makes it pretty clear she has realized what's up, and she does show she's really hard of hearing. Now, was Nancy the maid in on it is another question. I got the sense she might have been in cahoots to some degree.
Elizabeth was not in on the scheme. She's partially deaf, and that's probably why she was hired - so Gregory could go rooting around in the attic and pretend Paula was imagining any noise. The reason she does the above is because she is now wise to what Gregory is up to. Brian tells her to look after Paula - and lying to say that there had been no one in the house buys Paula some time. If Paula is thought to have imagined a man coming in, she's still safe. If a man actually has come in, that means Gregory knows the game is up.
Nancy also isn't in on the scheme. She's hired because she's so disagreeable that Paula won't get on with her and therefore won't have any allies. Gregory knows that Paula will a) disapprove of a flirty young woman who's not very respectable and b) suspect the girl could be flirting with her husband. That's another angle for Gregory to discredit her with ("she thinks I'm having an affair with the servant girl").
