You can scale the effect of fields, collisions, springs, and goals on particles. To scale the effects of dynamics, select the particle object, display the Attribute Editor, and set the Dynamics Weight to a value between 0 and 1.
A value of 0 causes fields, collisions, springs, and goals connected to the particle object to have no effect. A value of 1 provides the full effect. A value less than 1 sets a proportional effect. For example, 0.6 scales the effect to 60% of full strength.
Expressions are unaffected by Dynamics Weight.
A particle object has a Conserve attribute that influences the motion of particles whose velocity or acceleration attributes are controlled by dynamics (including particle expressions).
The Conserve value controls how much of a particle object's velocity is retained from frame to frame. Specifically, Conserve scales a particle's velocity attribute at the beginning of each frame's execution. After scaling the velocity, Maya applies any applicable dynamics to the particles to create the final positioning at the end of the frame.
Conserve doesn't affect motion created by keyframes. Keyframes affect only a particle object's worldVelocity attribute, not its local velocity attribute.
If you set Conserve to 0, none of the velocity attribute value is retained. The velocity is reset to 0 before each frame. At the end of each frame, the velocity is entirely the result of dynamics applied during that frame.
If you set Conserve to 1, the entire velocity attribute value is retained. This is the real-world physical response.
If you set Conserve to a value between 0 and 1, a percentage of the velocity attribute value is retained. For example, if you set Conserve to 0.75, each frame Maya first reduces the velocity attribute 25%, then it calculates any dynamic or expression effects on the object.
The above information comes directly from the manuals. Since you have already tried controlling the goal weight, I would highly recommend playing around with the Conserve attribute. When playing with Goals, I have found tweaking the Conserve and the goal weight I'm able to get the results that I'm looking for. You may also have to play with the Rate and Speed of the emitter! Good Luck!
Greg Bacon
Space Telescope Science Institute