Specify widths and heights of plots with grid.arrange

Try plot_grid from the cowplot package:

library(ggplot2)
library(gridExtra)
library(cowplot)
p1 <- qplot(mpg, wt, data=mtcars)
p2 <- p1
p3 <- p1 + theme(axis.text.y=element_blank(), axis.title.y=element_blank())
plot_grid(p1, p2, p3, align = "v", nrow = 3, rel_heights = c(1/4, 1/4, 1/2))

with gtable you need to set the heights of the panels manually,

g1 <- ggplotGrob(p1)
g2 <- ggplotGrob(p2)
g3 <- ggplotGrob(p3)

library(gridExtra)
g <- rbind(g1, g2, g3)

set_panel_heights <- function(g, heights){
  g$heights <- grid:::unit.list(g$heights) # hack until R 3.3 comes out
  id_panels <- unique(g$layout[g$layout$name=="panel", "t"])
  g$heights[id_panels] <- heights
  g
}

g <- set_panel_heights(g, lapply(1:3, grid::unit, "null"))
grid::grid.draw(g) 

Although a bit verbose, this approach is more general than specifying relative heights: you can mix all sorts of grid units,

grid::grid.newpage()
g <- do.call(rbind, replicate(3, ggplotGrob(ggplot()), simplify = FALSE))
g <- set_panel_heights(g, list(unit(1,"in"), unit(1,"line"), unit(1,"null")))
grid::grid.draw(g)