MDF and particle board are typically in the same density range as solid timbers. Some composites are lighter than some timbers but the reverse is also true, especially if looking at cheaper solid timber furniture that is often made of softwood like pine that is fairly low density.
The reasons for its use are as you say uniformity and ease of manufacture but also price. In particular for panels composites are readily available, cheaper and more stable re changes in humidity where for timber the converse of those characteristics. The availability of composite panels allows for simpler joining than solid timber. There is a whole family of fasteners for such panels including the famous Ikea systems that permit home assembly without glue in most cases.
Not really. For furniture that is made of the same stock throughout the centre of gravity depends on the geometry of the structure not its density. So if you had a tallboy made of pine (500g/l) and one of the same design and thickness made of hardwood (800g/l) the latter would weigh 60% more and be stronger, more durable and stiffer but its CoG would be in exactly the same place in the structure.