id <- c(rep(1, times = 10), rep(3, times = 10), rep(4, times = 10))
time <- c(1,2,3,4,5,6,7,8,9,10)
weight <- runif(30, min = 50, max = 100)
dataframe <- data.frame(id, time, weight)

coef(lm(weight~time, data = dataframe))[2]

sapply(split(dataframe, dataframe$id), function(i) coef(lm(weight ~ time, data = i))[2])
#     1.time      3.time      4.time
# 1.48800159 -0.05921987 -2.57523482