Unfortunately I can't explain why it happens (chemistry resembles voodoo sometimes) , but the density peak is for real.
Ullman's Encyc. of Ind. Chem. says:
'At constant temperature, the density of sulfuric acid increases steeply with rising H2SO4 concentration, reaching a maximum at about 98 %. From there up to a concentration of 100 % the density decreases slightly, but it rises again in the oleum range up to a concentration of ca. 60 % free SO3.'
Also I have table of densities at 20°C issued by a company which shows the same trend.
I neglected to mention in my previous post that using density as an indicator of composition is only useful up to about 95% H2SO4 for this reason. That is, if you measure a density of 1.838 say, then it could be either 100% or about 94% H2SO4 - you wouldn't know.
[That was nicely spotted Archaeoptrix.]