The best definition I have come across for the heavy ball so far is a shot which hits your racquet at a high speed. Basically, I think heaviness is a measure of how much energy you need to exert to resist the motion of the incoming ball and hit it back to the opponent. Thus, a fast paced and flat shot can be heavy because it will hit your racquet at a high speed. On the other hand, a slower shot, but with more topspin, may still hit your racquet at the same speed because the topspin causes the ball to slows down less when it bounces. The two shots may have different pace, but their heaviness could end up being the same. Remember, the key thing about this definition is the speed of the ball as it hits your racquet, not the speed of the ball when it left your opponent's racquet. That is why Nadal's forehand, which isn't the fastest shot in the men's game, is incredibly heavy, because the spin on it means his shots don't decelerate much after bouncing, causing them to hit the opponent's racquet at a high speed. And Safin's shots, which don't have that much spin, can be just as heavy, because they're just him damn hard and fast and the slowing down after the bounce isn't enough to mean it becomes a 'light' ball.
Therefore, I have no idea why you think Partner 2's shots are heavier, because if they are hit at the same pace, the shot with more spin should be heavier as it will slow down less after the bounce and hence hit your racquet at a higher speed. The only reason I can suggest is that human error means that although you feel like both shots are hit at the same pace, they actually aren't. Either that, or your judgement of the spin is inaccurate.
And therefore to answer your question of whether there is such a thing as a fast and heavy ball: yes there is, in two scenarios:
1) Safin-esque shot. Fast, not much spin, but so fast, it's heavy.
2) Federer type shot. Maybe not as hard hit as Safin's, but still fast, and because there's so much spin, it hits the opponent's racquet at the same speed as Safin's shot, so it still ends up being heavy.
Nadal's shots are heavy, but I wouldn't classify his normal, loopy rally forehand as being fast. When he flattens it out, then yes, it's both fast and heavy because of the combination of spin and pace. Otherwise, he just hits a heavy ball, not necessarily a particularly fast one.
"The greatness of a player is not measured by how he does against Federer." - dropshot winner