Think the word "weeny" is of recent vintage? Think again. Amanda Foreman records its use by none other than Massachusetts Senator Charles Sumner in the summer of 1861, referring to Secretary of State William H. Seward, whom Sumner detested. On July 3, 1861 The Times correspondent William Howard Russell
bumped into [Sumner] on the street [in Washington] and had to stand for an hour in the blistering heat while Sumner gleefully enlarged on "the dirty little mountebankism of my weeny friend in office."
So, was Sumner calling Seward a dick? Alas, probably not. A quick search around the internets suggests that the words "weeny" and "weenie" are of different origin. Weeny, an adjective, is a diminutive of "wee", small, and apparently dates to at least the late Eighteenth Century. Think "teeny-weeny." Weenie, a noun, apparently derives from wiener and is of later origin. Perhaps by association with weeny (I'm guessing here), "weenie" acquired a connotation of smallness (a weeny weenie, as it were) and thus the meaning of nerd.
About the illustration, entitled I'm Not to Blame for Being White, Sir! (1862):
Massachusetts senator and prominent antislavery advocate Charles Sumner is attacked here. The artist questions his sincerity as a humanitarian as he shows him dispensing a few coins to a black child on the street, while ignoring the appeal of a ragged white urchin. The scene is witnessed by two stylishly dressed young women. Though unsigned, the print has the relatively skillful draftsmanship and atmospheric quality found in the works of Boston lithographer Fabronius. See, for instance, that artist's "The Mower" (no. 1863-14). "The Secession Bubble" (no. 1862-12) also appears to be by Fabronius. Weitenkampf gives the 1862 date and publisher's imprint.