In this paper we explore the impact of birth weight on children's cognitive and behavioural outcomes using data from the UK Millennium Cohort Study. In order to deal with the endogeneity of birth weight we use an estimator based on the eliminant method. When coupled with ordinary least squares, this estimator allows us to bound the effects of birth weight. The results show that birth weight has significant but very small effects on male cognitive development at age 3 and on female cognitive and behavioural outcomes at age 3. We also find that birth weight affects age 5 outcomes only through previous achievements, and that the overall impact fades out over time. These findings call into question the effectiveness of birth weight as a policy target.