ggplot2: Map geom size to group means within data

Question

Is it possible to map an aesthetic to the mean value for each group in a dataset?

Example

Map the line width for each continent in gapminder, but avoid pre-processing the data to create the group means for this mapping. The following plot is the desired output:

library(ggplot2)
library(gapminder)

ggplot(data = gapminder %>% group_by(continent) %>% mutate(mean_pop = mean(pop)),
       mapping = aes(x = year,
                     y = lifeExp,
                     color = continent, 
                     linetype = continent,
                     size = mean_pop)) +
  geom_line(stat = "summary")

But I want data to just take gapminder as-is:

ggplot(data = gapminder,
       mapping = aes(x = year,
                     y = lifeExp,
                     color = continent, 
                     linetype = continent,
                     ...)) +
  geom_line(stat = "summary")