Steven's post from the Chicago Daily News corresponds with B&W's domestic rate book. It's not likely second class, because it would need to have been more than 4 ounces (although it's possible); third class seems more likely, paying a rate to accommodate something over 2 ounces. I know that third class would have been a mute cancel (which it is on the wrapper; not sure about second class).
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Second Class postage was used for newspapers and periodicals. For the time period of 1885 to 1915, your are correct that the postage rate was 1 cent per pound. I think it is conceivable that a newspaper or periodical from a larger city could easily weigh two pounds.
This link probably contains more information than you are looking for, but it does contain some interesting stuff.