I've hit on this in the comments to other posts, but one of the nice features of weighted density is that it permits us to compare apples to apples (even though the comparison may be royal gala to red delicious). Standard density is extremely sensitive to geographic boundaries. This is why most debates over density quickly turn into squabbles over the proper geographic unit. CMSA? MSA? Urbanized area? Central city? And then it's just a matter of time before someone brings up City X's moutains or parks or other uninhabitable land that drag down its density.
Because weighted density is determined by the density at which most people live, adding or subtracting land at the margin -- even a lot of land -- does not matter much unless the land contains a large chunk of the population. Weighted density does not depend on precisely how the geographic area is defined.
Example: In 2000, Houston's urbanized area had a population of 3,822,000 and a standard density of 2,951/square mile. Houston's Primary Metropolitan Statistical Area* had nearly four times the land area but only about 355,000 (10%) more people. (The PMSA has a lot of cows.) As a result, Houston's PMSA had a measley 706 persons per square mile, just a little over one person/acre.
The PMSA's weighted density, however, was a more respectable 4,296. That's only 5% off the urbanized area's weighted density of 4,514. Adding a bunch of cow pastures does not change the fact that the vast majority of the PMSA population was bunched at a much higher density.
The same holds for Portland. In 2000, its PMSA had a standard density of just 381/square mile. But the PMSA's weighted density was 3,943/square mile, down just 10% or so from the urbanized area's weighted density of 4,383.
Note that a lot of the vacant land around Houston is vacant simply because no one has gotten around to developing it yet. A lot of the land around Portland is vacant because of policies designed to preserve open space and slow sprawl. This difference is often a flash point for disagreements over geographic boundaries. Weighted density allows us to sidestep these arguments by focusing on the density at which the average person lives.
*A PMSA consists of one or more counties within an MSA that have substantial commuting interchange.