I know very little about Chalean Extreme so I can't comment on it, but LOVE NROL4W and I am on Stage 6. Maybe someone who has tried both can weigh in on this.

I want to be able to do it at home. How heavy weights will I need?

There are a few threads about equipment for home but a lot of people have been able to do it with adjustable dumbbells, exercise ball and a step up box. There's a way to adjust exercises to fit homes without a barbell or squat rack (like single leg squats/deadlifts with dumbbells for example) and I linked to a few ideas on a previous thread that shouldn't be more than 1 page back.
The NROL forum has a lot of great ideas/suggestions for home lifters.

Finished CLX and LOVED it...I was able to build a lot of strength with it but I didn't drop a ton of weight. I have NROL4W but haven't actually started it yet. I have done a few workouts but nothing steady since I'm currently doing another program. But from what I have looked at with this program you can totally do it at home. I have adjustable dumbbells that I purchased when I started the push phase of CLX and then I have a bar from Les Mills Pump. I do need to get a step though..I'm thinking step so I can double it as a bench/step and save a little room in the house.