Contemporary general circulation models (GCMs) and Earth system models (ESMs) are developed by a large number of modeling groups globally. They use a wide range of representations of physical processes, allowing for structural (code) uncertainty to be partially quantified with multi-model ensembles (MMEs). Many models in the MMEs of the Coupled Model Intercomparison Project (CMIP) have a common development history due to sharing of code and schemes. This makes their projections statistically dependent and introduces biases in MME statistics. Previous research has focused on model output and code dependence, and model code genealogy of CMIP models has not been fully analyzed. We present a full reconstruction of CMIP3, CMIP5 and CMIP6 code genealogy of 167 atmospheric models, GCMs, and ESMs (of which 114 participated in CMIP) based on the available literature, with a focus on the atmospheric component and atmospheric physics. We identify 12 main model families. We propose family and code weighting methods designed to reduce the effect of model structural dependence in MMEs. We analyze weighted effective climate sensitivity (ECS), climate feedbacks, forcing, and global mean near-surface air temperature, and how they differ by model family. Models in the same family often have similar climate properties. We show that weighting can partially reconcile differences in ECS and cloud feedbacks between CMIP5 and CMIP6. The results can help in understanding structural dependence between CMIP models, and the proposed code and family weighting methods can be used in MME assessments to ameliorate model structural sampling biases.