I mean my solutions are equivalent indeed. It was just by the example i found in the documentation that I figured it out; it is a bit sparsely documented... Metadata can be anything, even multiple things, so I guess you can make now your own function...

Hi Mark,

I think I spoke too soon; it IS parsed:

BubbleChart[{{1, 0, 1} -> Range[5], {0, 1, 2}, {1, 2, 3} -> RandomReal[1, 10]}, 
ChartElementFunction -> ((Print[{##}]; DataDrilldownBubble[{##}]) &)] 

Notice I put ## in there, it is parsed as multiple arguments not as a list of arguments; that was my mistake... I found out by checking out the code:

Needs["GeneralUtilities`"]
PrintDefinitions@Charting`iBubbleChart

and the dependencies.

So you can do it like this:

data = {{4, 1, 3} -> 7, {0, 9, 1} -> 1, {4, 5, 2} -> 5, {2, 3, 0.4`} -> 2};
data[[All, 2]] = Rescale[data[[All, 2]]];
ClearAll[g]
g[{xrange_, yrange_}, {x_, y_, z_}, meta_] := Style[Disk[{x, y}, z], ColorData["Rainbow"][First@meta]]
BubbleChart[data, ChartElementFunction -> g, AspectRatio -> Automatic]

As you can see, it seems to be ignored:

ClearAll[DataDrilldownBubble]
DataDrilldownBubble[{{xmin_,xmax_},{ymin_,ymax_}},v_,{meta_},style___]:=PopupWindow[Polygon[{{xmin,ymin},{xmax,ymax},{xmin,ymax},{xmax,ymin}}],PieChart[meta]];
DataDrilldownBubble[{{xmin_,xmax_},{ymin_,ymax_}},y_,___]:=Rectangle[{xmin,ymin},{xmax,ymax}];
BubbleChart[{{1,0,1}->Range[5],{0,1,2},{1,2,3}->RandomReal[1,10]},ChartElementFunction->((Print[#];DataDrilldownBubble[#])&)]

{{0.942265,1.05774},{-0.11547,0.11547}}
{{-0.0816497,0.0816497},{0.836701,1.1633}}
{{0.9,1.1},{1.8,2.2}}

However you can also do it yourself in the following way:

data={{4,1,3,7},{0,9,1,1},{4,5,2,5},{2,3,0.4,2}};
data[[All,4]]=Rescale[data[[All,4]]];
BubbleChart[data[[All,;;3]],ChartElements->Table[Graphics[{ColorData["Rainbow"][d],Disk[{0,0},1]}],{d,data[[All,4]]}],BubbleSizes->{0.05,0.15},ChartLabels->Placed[countries,Tooltip],FrameLabel->properties[[1;;2]]]