Read the data into R using x <- read.csv(filename). Make sure the dates come in as character class and weight as numeric.
Then use the following:

require(zoo)
require(forecast) # Needed for the ses function
x$date <- as.Date(x$date,"%m/%d/%Y") # Guessing you are using the US date format
x$weight <- zoo(x$weight,x$date) # Allows for irregular dates
plot(x$weight, xlab="Date", ylab="Weight") # Produce time plot
ewma <- as.vector(fitted(ses(ts(x$weight)))) # Compute ewma with parameter selected using MLE
lines(zoo(ewma,x$date),col="red") # Add ewma line to plot

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