My answer assumes that you're looking to end the relationship no matter what. If you think you may want to salvage it, or you have second thoughts, this may not be the best approach to take.
The situation you're in is quite sensitive. On one hand you feel as if the relationship is essentially dead and wish to move on. On the other you don't want to pile additional stress on your girlfriend in light of her father's recent passing.
It seems clear that following the events detailed in your previous post, the relationship is on its last legs. Furthermore, it also seems like there were elements to it that were not sitting well with you in the first place (which influenced your previous decisions). You've made up your mind regarding wanting to move on, and at this point you're only still there because you want to be considerate toward her.
My personal opinion is that although she's still leaning on you (perhaps due to familiarity, or perhaps due to proximity), the outcome of the situation is not really in doubt. Once a couple of weeks have passed since the funeral, and the initial shock of the situation has worn off, I'd make my move.
The most important part here is not necessarily your timing (2 vs 3 weeks doesn't really matter IMO), but more the content of your message, and the way you deliver it. She will still be missing her father regardless of whether you're around or not. The point here is that you probably can't lessen the pain of the passing in any way. You can only be considerate in how you part ways.
Sit her down for a private talk, and be honest with her. Say that you feel that the relationship is irreparably broken, and that you think it would be best to part ways. If you think you'd be open to trying to rekindle things, mention that you're open to trying to rebuild trust, but that in the mean time you will be moving out, and leaving her the apartment. Make sure to underline that you'll be there if she wants to talk, or needs any help, but that you will be out of the apartment by [deadline here].
I would keep the initial message short, and base any follow ups on her reaction. She may simply nod, and say she agrees. Or she may ask you why you're giving up on her, etc. Be prepared to elaborate.
Try to remain calm and collected at all times. Don't raise your voice, and don't change your mind. It's worse to say you're moving out and not follow through, than it is to move out, then move back in if things improve. Remember that you're moving out because the current situation is making both of you (and especially you) miserable.