WordWeb Online

1. Ingratiate oneself to; often with insincere behavior
   "She is cozying up to the chairman";
   - cotton up [archaic], play up [informal], suck up, cosy up [Brit, Cdn]
    
2. Move or arrange oneself in a comfortable and cozy position
   "We cozied up against each other to keep warm";
   - cuddle, snuggle, nestle, nest, nuzzle, draw close, cosy [Brit, Cdn], cozy [N. Amer], cosy up [Brit, Cdn]

Derived forms: cozied up, cozies up, cozying up

Type of: cling to, clutch, hold close, hold tight, ingratiate