Say we have a container of water full to the brim and some object with volume $V$. We measure the mass of the container with the object by its side to obtain $m$. Now we put the object inside the container and it sinks, and we measure the mass of the container with the object in it to obtain $m_1$. Now, since the container is full to the brim, when we put the object inside, it will push out a volume $V$ of water, but also because of the buoyant force the objects weight will be less for the mass of the displaced water so we can conclude that $m-m_1=2\rho gV$ where $\rho$ stands for water density. Is this correct?
What happens if the object floats? Will then the measured mass be $m-\rho g \Delta V$ where $\Delta V$ is the volume of the object submerged/volume of displaced (pushed out) water?