Cerquita is the diminutive form of cerca, meaning "close". The addition of -ita intensifies the meaning, conveying "very close" or "so close".
In the song, the phrase "Tan cerquita que te tuve y te perdí" (So close I had you and I lost you) beautifully expresses the bittersweet regret of having someone incredibly near, almost within reach, only to let them slip away. It's a common and endearing way to add emphasis in Spanish.
Aleks Syntek's "Tan Cerquita" ("So Close"), with Cristian Castro, is about spotting a love you missed while it was standing right in front of you. The narrator counts every question he never asked a friend he'd shared libraries and coffee cups with -- "Nos colgaron de la misma luna" ("We were hung from the same moon") -- insisting for years that what he felt was only friendship, "Donde yo solo veía a una amiga" ("Where I only saw a friend"). By the time he can finally name it -- "Tan cerquita que te tuve y te perdí" ("So close I had you and I lost you") -- she's already gone, and all that's left is the refrain of a chance he let pass in plain sight.