If I'm understanding you correctly it sounds like you want to take a sample of size 5 and then take the mean, so something like this:
mean(sample(Weight$Weight, size = 5)
But then you want to do that 1000 times. So then you could use the replicate() function:
rep.out <- replicate(n = 1000, mean(sample(Weight$Weight, size = 5)))
For the sample size of 10, replace size = 5 with size = 10.