Creating a smoothed heat map with normalized frequencies per column

Question

I am studying the relationship between the concentration of a metabolite (hypocretin) and a continuous outcome variable (BMI). I want to create a frequency heat map in which different concentrations of the metabolite are presented on the X-axis and the frequency of different BMI values on the Y-axis. I have found an unrelated picture on the Internet that I modified in photoshop to represent what I would like to create.

I want to get a heatmap with the following attributes:

1. Smoothed graph

2. The heat map shows the proportion of values ​in their respective columns, which means that the frequency of each column adds up to 1, instead of the frequency of values in all columns combined.

When I visualize the heat map with our data using ggplot2 this results in the following heat map (corresponding to code1 below).

#code1

BMI_HEATMAP<- df3 %>%
  ggplot(., aes(x = Hypocretin.level, y = BMI, height = 1,width=1)) + 
    geom_density_2d_filled()+ 
  labs(title = 
         "Heat Map of the Effect of Hypocretin.Level on Body Mass Index",
       subtitle =
         "Where BMI ranges between 0 and 60 with 18.5 - 24.9 being considered healthy (UK National Health Service, 2020)",
       x="Hypocretin Level/pg/mL(1:0-40;2:40-110;3:110-200;4:200+)", 
       y="Body Mass Index (BMI)")+
  scale_x_continuous(breaks = c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18)) +
  scale_y_continuous(breaks = c(10,20,30,40,50,60)) +
  mytheme1
BMI_HEATMAP

heat map with smoothing but not normalized per metabolite concentration:

Unfortunately for some of the neurometabolite concentrations I have a lot of data points available (1 and 18) but for the other concentrations (2-17) I have much less data points available. I am however mainly interested in these (sparse) intermediate values and would therefore like to normalize the frequencies per metabolite concentration (in such a way that each concentration [or column] adds to 100% frequency) to better visualize a possible trend.

I then used the following ggplot2 code that normalizes the frequency per metabolite concentration (code2).

#code2

  BMI_dot_plot2 <- df3 %>%
       ggplot(.,aes(x = Hypocretin.level, y = BMI, fill = freq, height = 1,width=1))+
       labs(title = 
                             "Heat Map of the Effect of Hypocretin.Level on Body Mass Index",
                      subtitle =
                            "Where BMI ranges between 0 and 60 with 18.5 - 24.9 being considered healthy (UK National Health Service, 2020)",
                      x="Hypocretin Level/pg/mL(1:0-40;2:40-110;3:110-200;4:200+)", 
                      y="Body Mass Index (BMI)",
                      fill = " Freq")+
       geom_tile(colour="white", size=0) +
    scale_x_continuous(breaks = c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18)) +
    scale_y_continuous(breaks = c(15,20,30,40,50)) +
       scale_fill_viridis()+
       mytheme1
  BMI_dot_plot2

heat map with normalization per metabolite concentration but no smoothing:

This code however does not have smoothing included, which makes the graph difficult to interpret.

What code should I use to have the frequencies normalized per neurometabolite concentration to 100% frequency (like in code2) but also have the data smoothed that it looks like the heat map in the first picture of code 1?