The weighted die model has increased probability on 6,5, and 4 (in that order).

You need to pause the print just past halfway through the cavity so you can embed your weight. I used a 5/16" steel ball bearing with a drop of white glue to hold it in place (and not rattle XD).

You can change how 'loaded' it is by modifying your infill. At 100% you probably wouldn't notice the weight difference much, but at 20% it seems to work much better. It's not 100% gonna land on what you want, but if it did that then no one would believe it's not a loaded die.

Given that the nozzle has a 45 degree angle, it's impossible to fill in the area right next to a ball bearing if it's in the half made cavity, hence the odd partial cone shape near the equator. Due to the size and shape, the cavity won't work as well in the opposite corner (to favor 1's).

Instead I've added additional models that have custom infill to favor high numbers or low numbers. Print these at 100% infill to get the best effect, though I don't think they work as well as a die with an embedded metal weight.

Modeled in Blender. If you want to change the weights, the negative infill boxes are on the 4th layer.

FILES:
LoadedDie - Weighted die with cavity for ball bearing

LoadedDie2_1 - Custom infill die favoring low numbers

LoadedDie2_6 - Custom infill die favoring high numbers