The combination of "Twitter" and "Serious" to invoke a strong emphatic meaning towards a statement being Tweeted on Twitter.
In reference to something being said on Twitter:
-A Tweet of, showing, or characterized by deep thought.
-A Tweet of grave or somber disposition, character, or manner.
-A Tweet being in earnest; sincere; not trifling.
-A Tweet requiring thought, concentration, or application.
-A Tweet weighty or important.
-A Tweet giving cause for apprehension; critical.
Him: "I just saw Ben tweet that he actually prefers Coors over Pabst Blue Ribbon."