"It was so very large that we had no place in the house to fix it...instead therefore of gratifying our vanity...there it leaned in a most mortifying manner against the kitchen wall...the jest of all our neighbors".

I found part of the story to be quite humorous and think that maybe the portrait is some sort of metaphor for the Primrose family. They are interacting with Mr.Thornhill, hoping to make a match that is above and beyond their station, rather than looking at some of the men who would more closely match their social position. In other words, they're too big for their britches :), just as their portrait with its huge size and grand allusions to Alexander the Great and Venus cannot be gotten through the small doorway of their small house.