Again, why? Is there any reason to think that late life BMI will inversely correlate with BMI such that the old fat people were actually the skinny young people? If it's just measurement error, then it's no worse than most variables which get used in health or sociology research.
> If you can't see selection at high effect alleles I'm not sure you'll be able to detect them in aggregate either, especially with very noisy phenotype data.
All of these are highly polygenic traits. A 'high effect allele' means explaining 1% or less of variance. Selection on such a trait is going to shift the frequency by a tiny amount. Grossly underpowered individually. You have to consider them jointly. Noisy phenotype makes that more, not less, true.