We introduce a family of weighted BMO spaces in the Bergman metric on the unit ball of $\Bbb{C}^n$ and use them to characterize complex functions $f$ such that the big Hankel operators $H_f$ and $H\overline{_f}$ are both bounded or compact from a weighted Bergman space into a weighted Lesbegue space with possibly different exponents and different weights. As a consequence, when the symbol function $f$ is holomorphic, we characterize bounded and compact Hankel operators $H\overline{_f}$ between weighted Bergman spaces. In particular, this resolves two questions left open in [7, 12].