Re: Economic 'weight' of different regions - is Egypt under represented?
From the source already mentioned, "Egypt and Syria in the Fatimid, Ayyubid and Mamluk eras" by U. Vermeulen and D. De Smet, it's written that the population in Egypt remained static or increased at a slow rate. For the whole medieval period that population was estimated between 4 and 5 millions inhabitants in average, fluctuating irregularly between 3 and 6 millions because of epidemics, starvation, etc...
Just to compare, below some figures given by Josiah C. Russell, "Population in Europe:, in Carlo M. Cipolla, ed., The Fontana Economic History of Europe, Vol. I: The Middle Ages, (Glasgow : Collins/Fontana, 1972), 25-71:
Under the patronage of Flinn, proud patron of Jadli, from the Heresy Vault of the Imperial House of Hader