The relevant definition in the (unlinkable) OED is: "Virtually, substantially; so far as the result is concerned." The historical examples go back to 1844:
1844 J. Mackintosh Life T. More in Wks. (1846) I. 442 It is not equitable to treat him as effectively..answerable for measures of state.Don't mix up this usage with the more literal meanings: "So as to produce an effect, esp. a desired effect; (emphatically) with powerful effect; decisively, completely," and "So as to produce a (pleasing or remarkable) aesthetic effect." Examples of that meaning:
1884 Harper's Mag. Oct. 796/2 Effectively England is a republic and not a monarchy.
1878 R. W. Dale Lect. Preaching (ed. 3) vi. 163 If we can preach without reading, we are likely to preach more effectively.I searched the NYT archive for "effectively" and found plenty of examples of the literal use: "Using Dashes Effectively" ("When do you use a dash? What is an em-dash? What about an en-dash? Is a dash the same as a hyphen?"), "Collecting Taxes, Effectively," etc.
1857 H. Spencer in Fraser's Mag. Oct. 401/2 This tremulousness of voice is very effectively used by some vocalists.
But the weasel-word usage abounds: "After Verbal Fire, Senate Effectively Kills Climate Change Bill," "New Law in Egypt Effectively Bans Street Protests," "4-3 Ruling Effectively Halts Death Penalty in New York," "Pro-Choice Doesn't Force Abortions on Women; U.S. Effectively Decides," etc.
Please be careful reading.