No, you are really not.
For those of you big guys who do not have to consider how much things actually weigh, and are only worrying about buoyancy in water, it is easy to forget that a stainless backplate is actually VERY heavy. That is why it can replace weight elsewhere. That's weight that is on the diver on the weight belt, integrated weights, or in the backplate or in the tank.
Any way, it is just weight on the diver. It is just shifting the weight around.
The total weight of dive gear dry for a BP/W is much heavier, ignoring the weights. With the weights, it's a push.
Every time this comes up, it seems worth pointing out that for all BP/W strengths, it is far from mainstream for some very good reasons. It's not just some "They don't want you to know you" conspiracy by dive manufacturers to put divers in ineffective gear. And there is the ongoing hidden effect that people 1. dive more and become better divers and 2. sometimes then switch to BP/W, and forget that it is part one that makes them better divers not part two, that always gets lost in people's enthusiasm to act as evangelist for their gear choices.
This evangelizing for BP/W's here at SB always comes across as some sort of Mac/Windows fanboy arguing. The solution to viruses on computers is not "Get a Mac" and the solution to BCD choices is not "Get a BP/W". The solution to any question is always more nuanced.