dplyr count within subgroup

I have the following data frame:

df<-data.frame(Date=rep(x=as.Date(c("2016/01/01", "2016/01/02")),each=12),
       Group=rep(x=c("G1","G2"),each=6,times=2),
       ID=rep(c("G1F1","G1F2","G1F3","G1M4","G1M5","G1M6","G2F1","G2F2","G2F3","G2M4","G2M5","G2M6"),times=2),
       Gender=rep(c("Female","Male"),each=3,times=4),
       Weight=c(c(100,100,100,100,120,140),rep(c(100,120,140,100,100,100),times=2),c(100,100,100,100,120,140)))

I would like to create a new column CountComp that displays the count of same gender same group member counts of individual whose weight is within 10 gram above or below the weight of the individual specified in each row on a given date such as to get:

df2<-data.frame(Date=rep(x=as.Date(c("2016/01/01", "2016/01/02")),each=12),
           Group=rep(x=c("G1","G2"),each=6,times=2),
           ID=rep(c("G1F1","G1F2","G1F3","G1M4","G1M5","G1M6","G2F1","G2F2","G2F3","G2M4","G2M5","G2M6"),times=2),
           Gender=rep(c("Female","Male"),each=3,times=4),
           Weight=c(c(100,100,100,100,120,140),rep(c(100,120,140,100,100,100),times=2),c(100,100,100,100,120,140)),
           CountComp=c(c(2,2,2,0,0,0),rep(c(0,0,0,2,2,2),times=2),c(2,2,2,0,0,0)))

I am very new to R and thought that dplyr could offer a solution using group_by and mutate function, but have so far failed in finding one.