I think the real issue is the poor rolling + the weight of the dice.
With regular dice, that casual rolling would be fine, because the dice would bounce off the table more, introducing chaos. You could probably drop a regular die directly down, with 6 up every time, and get pretty random results.
With this die, I’ll bet if you did that you’d get much less random results.
So honestly, I think the question of whether the die are fair or not is actually a canard. Even if they were weighted, they bounce so little that it mostly depends on what face it fell on, not what side weighs more.
Since you pick it up and roll the same way each time, you’re probably getting into some kinds of cycles, such that patterns show up. This in turns leads those numbers to be over-represented in your final table.
So then it just comes down to your rolling. The final result will be as random as your roll is.
My prediction: if you did this another 300 times, with the same technique, you’d still get biased-looking numbers, but they will be different numbers.
If you roll it around properly in a cup, you’ll get random numbers.