The Structure Theorem of Tropical geometry states:
Let $X$ be an irreducible $d$-dimensional subvariety of $\mathbb T^n$ . Then $\operatorname{trop}(X)$ is the support of a balanced weighted $Γ_{\rm val}$ -rational polyhedral complex pure of dimension $d$. If $\operatorname{char}(K) = 0$ then this complex is connected in codimension-one.
What does the term "balanced weighted polyhedral complex" mean in the above theorem?
And suppose I have a subvariety of the algebraic torus. How do I determine the weights of its tropicalization?
