Incidence rates with weights and confidence intervals

Question

Say you have sample data,

data = data.frame(id=c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17),
start=c(58,58,59,29,28,38,53,57,40,33,37,43,54,46,37,60,39),
stop