Mecías comes from the verb mecer, which means to sway, rock, or cradle. It evokes a gentle, almost dreamlike movement.
In "Lo Dudo," Cristian Castro uses this word to paint a picture of the past, singing, "Conmigo te mecías en el aire" (With me, you swayed in the air). It beautifully conveys a sense of freedom, lightness, and intimate connection that he believes his former lover won't find with anyone else. It's a poetic and tender word that stands out in the lyrics.
Cristian Castro plays the ex who insists he's fine with it, and then spends the whole song proving he isn't. He keeps pushing her out the door with "Anda y ve" (go on, go), "Te está esperando" (he's waiting for you), and even "No lo hagas por mí, que al fin y al cabo somos solo amigos" (don't do it for me, after all we're just friends). Al fin y al cabo means "after all" or "when all is said and done", and you'll hear it everywhere in Spanish.
Then the mask slips. He hopes she feels with the new guy "lo que en su día tú sentías conmigo" (what you once felt with me), en su día being a handy way to say "back then". "Pero lo dudo" (but I doubt it), he adds, and the title lands. He remembers how "conmigo te mecías en el aire" (with me you swayed in the air) and how she even cried over a kiss, "llorando de alegría y no de miedo" (crying from joy, not from fear). His final jab, "Y dudo que te pase igual con él" (and I doubt the same will happen to you with him), is pure wounded pride, and it's very hard not to sing along with it.