Not significantly, no. Individual tolerance (even in opiate-naive people with no aquired tolerance) is the biggest factor. Weight may have some role (height/general body size as opposed to fat tissue is likely to be more significant) but doses are never calculated this way as it is unreliable and highly variable. Always go by your tolerance, or assume you have a very low tolerance if you have not tried opiates before (you can ask on here about suggested safe doses..)
Apart from tolerance, other factors influencing opiate dose and effects include liver and kidney disease.