Big-Up: To praise or promote; to raise the profile of. Urban Dictionary gives eight citations going back as far as 2003. Usage example: "I want to big-up everyone who has supported me over the years."
Lexicographer Ben Zimmer, writing last week in From A to Zimmer, an Oxford University Press blog, notes that the term comes from Caribbean English and is gaining popularity in North America:
Three recent quotes from American media sources give you a sense of how it’s being used these days. Here’s the actress Jaime Pressly critiquing the show “Ugly Betty”: “They’re purposefully big-upping the ugly fat girl to make everybody feel great, but it also glamorizes the fact that people are getting plastic surgery because they can.” The music blog Idolator had this to say about an “American Idol” contestant: “This is actually the second time that Hennessy has been big-upped by the Idol powers that be,” adding, “is big-upping this girl really the best strategy to boost ratings?” And finally a profile of Staten Island’s Budos Band notes: “Legit blogs like Brooklyn Vegan and online publications like Pitchfork and RollingStone.com have also big-upped the band.” ...
Note that Jaime Pressly said that “Ugly Betty” was “big-upping the ugly fat girl,” not that the show was “bigging up the ugly fat girl” (or “bigging the ugly fat girl up“). So we find that big-up is being treated as a single entity that can be inflected with verb endings, rather than as the verb big plus the particle up. This also helps explain why the hyphenated form is appearing so commonly in print. It’s a bit unusual to find a so-called “phrasal verb” (also known as a “verb-particle construction”) undergoing this type of reanalysis, but one similar case is voice over meaning ‘to supply unseen narration to a broadcast.’ A film can be voiced over or it can be voice-overed, depending on whether voice over is treated as one entity or two. Of course, the existence of the noun voice-over helps with the single-entity reading, just as the noun big-up encourages inflected forms like big-upping.