Work in a stable theory (or more generally a simple theory) . The preweight of a complete type 
 is defined to be the supremum of the cardinals 
 such that there is some 
-independent set 
 such that 
 forks with 
 for every 
, i.e., 
 for every 
. This is well-defined, and in fact the preweight of 
 is bounded above by the 
 appearing in the local character of forking (which is 
 for superstable theories).
If  is a stationary type, the weight of 
 is defined to be the largest weight of any non-forking extension of 
. 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.) ::: ::: :::