Sorry about this. That post is old and the arguments have changed.

Try this instead

fit2 <- euler(c(A = 16971, B = 218, C = 215, 
                "A&B" = 112, "A&C" = 112, "B&C"= 51,"A&B&C" = 23))
plot(fit2,
     fills = c("dodgerblue4", "darkgoldenrod1", "cornsilk4"),
     edges = FALSE,
     fontsize = 8,
     quantities = list(fontsize = 8))

As explained in the comments, you will not be able to express an arbitrary set of relationships for more than 3 sets with circles. The package eulerr uses ellipses to get more combinations and also make the result somewhat proportional to the number of elements in each region. I made a different package called nVennR that uses circles for the regions instead of the sets. The sets are then drawn around those circles:

> library(nVennR)
> myT <- read.table('clipboard', header = T)
> lol <- as.list(myT)
> myV <- plotVenn(lol)
> myV <- plotVenn(nVennObj = myV)
> myV <- plotVenn(nVennObj = myV)
> myV <- plotVenn(nVennObj = myV)
> myV <- plotVenn(nVennObj = myV)
> myV <- plotVenn(nVennObj = myV)
> myV <- showSVG(nVennObj = myV, opacity = 0.2)

Repeating the command myV <- plotVenn(nVennObj = myV) is necessary to get a compact shape. If you try it, you will see that it takes a couple of minutes, as it needs to perform several simulations. The package can take any number of sets, but things get really slow above 9 sets. The result:

You can save, edit and improve the picture to better show the information, but it is not trivial. You can find more information in the vignette.

Regarding how to fix the issue, it depends on the level of precission you want. From the nVenn algorithm, I authored the nVennR package to create quasi-proportional Euler diagrams. With the caveats mentioned in the link, you can represent larger numbers of sets and show the relative size of each region. In your example,

library(nVennR)
myV <- createVennObj(nSets = 4, sNames = c('A', 'B', 'C', 'D'), sSizes = c(0, 26, 53, 7, 22, 5, 16, 3, 54, 10, 29, 4, 20, 5, 14, 3))
myV <- plotVenn(nVennObj = myV)

And the result would be:

Depending on your requirements, this may not be satisfactory. The proportionality is in the area of the circles, not the regions (you can see that the region 1, 2, 3, 4 - A&B&C&D - has empty space. However, this strategy overcomes the limitations of regular shapes in these representations mentioned by Johan Larsson. If you are interested, there are more details in the vignette.