Work in a stable theory (or more generally a simple theory) {\displaystyle T}. The preweight of a complete type {\displaystyle \operatorname {tp} (a/C)} is defined to be the supremum of the cardinals {\displaystyle \kappa } such that there is some {\displaystyle C}-independent set {\displaystyle \{b_{\lambda }:\lambda <\kappa \}} such that {\displaystyle a} forks with {\displaystyle b_{\lambda }} for every {\displaystyle \lambda }, i.e., {\displaystyle a\not \downarrow _{C}b_{\lambda }} for every {\displaystyle \lambda }. This is well-defined, and in fact the preweight of {\displaystyle \operatorname {tp} (a/C)} is bounded above by the {\displaystyle \kappa } appearing in the local character of forking (which is {\displaystyle \aleph _{0}} for superstable theories).

If {\displaystyle p} is a stationary type, the weight of {\displaystyle p} is defined to be the largest weight of any non-forking extension of {\displaystyle p}. Types of Morley rank 1, or more generally, Lascar rank 1 have weight 1. More generally, regular types have weight 1.

Weight is generalized to simple theories in a straightforward way. Weight is generalized to NIP theories by the notion of dp-rank, and is generalized to NTP2 theories by the notion of burden.

Superstable theories have plenty of weight 1 types, in some sense… (Every type is domination equivalent to a product of weight 1 type. Also, every type has finite weight.) ::: ::: :::