The term "weight" is misused, as weight, by definition, is how hard gravity pulls on something. If I were on the moon, I would weigh less than here on earth. However, MASS is clearly positively correlated to weight, and that is where the common confusion comes from. No matter where I stand, on earth, on the moon, or in zero-G, my mass remains the same. A ship with greater mass takes more energy to move a larger object than a smaller, and it would take more energy to overcome inertia and redirect motion. Thus, a smaller, lower mass ship would accelerate faster and be more maneuverable.

Incidently in a zero-G vacuum, there should be no speed limit, except those brought on by relativity as you approach the speed of light (of course in Star Wars, hyperspace allows for faster than light travel, so I won't address that aspect). All ships could ultimately go equally fast, no matter how large they are or how powerful their engines. What makes a difference is their acceleration. Lower mass and more powerful engines would result in reaching your desired speed faster, but any ship that kept at it would not be hindered with a top speed.