Your data is in 'wide' format, but ggplot works best with data in 'long' format (also called 'tidy' format).
It is entirely reasonable to be a little confused over this when first coming to ggplot. Still, there are many advantages to using a long format when it comes to using ggplot.
The general approach to this type of issue is to transform the data before you send it to ggplot.
In the suggestion below, I create some sample data that mimicks the data you have linked to. I then transform the data to a long format and plot it using ggplot.
In the end, there is a solution without transforming the data. It will likely appear more straightforward as first. Still, I recommend that you use the first solution, as it will probably work better for you as your project becomes more complicated.
library(tidyverse)
set.seed(1)
# Sample Data, generated to mimic the data you linked to
Lifts <-tibble(
Large = rnorm(500, mean = 105.872, sd = 10.074),
Small = rnorm(500, mean = 105.506, sd = 10.227))
# This is what the sample data looks like
head(Lifts)
#> # A tibble: 6 x 2
#> Large Small
#> <dbl> <dbl>
#> 1 99.6 106.
#> 2 108. 102.
#> 3 97.5 93.4
#> 4 122. 106.
#> 5 109. 116.
#> 6 97.6 122.
# Tranform lifts into long format
Lifts_long_format <- Lifts %>%
pivot_longer(cols = everything(), names_to = "size")
# This is the structure
head(Lifts_long_format)
#> # A tibble: 6 x 2
#> size value
#> <chr> <dbl>
#> 1 Large 99.6
#> 2 Small 106.
#> 3 Large 108.
#> 4 Small 102.
#> 5 Large 97.5
#> 6 Small 93.4
ggplot(Lifts_long_format, aes(value, fill = size))+
geom_density(alpha = 0.5) +
labs(x = "Median of Weight", y = "Distribution of Data")

# You can also do it without transforming the data
ggplot(Lifts)+
geom_density(aes(Large), fill = "blue", alpha = 0.5) +
geom_density(aes(Small), fill = "red", alpha = 0.5) +
labs(x = "Median of Weight", y = "Distribution of Data")

Created on 2020-02-20 by the reprex package (v0.3.0)