The short answer to your question is, "yes, weight does affect cruising speed on the flat, but not by much."
The longer answer to your question is a special case of one of the answers given to this bicycles.stackexchange question: "How can one estimate drag for a bicycle?" There you can find the equation for power given speed, disaggregated into the components for aerodynamic drag, rolling resistance, acceleration, and climbing (or descending). In your case, you are only interested in the components of drag that are affected by a change in mass.
You have asked about "on the flat" so we can ignore the climbing or descending component.
You have asked about "cruising speed" so we can ignore the acceleration component.
If you look at the drag equation, mass does not enter into the aerodynamic component.
The only component of drag, then, that is affected by mass is the rolling resistance component. Rolling drag force is Crr * m * g where Crr is the coefficient of rolling resistance, m is the total mass, and g is the gravitational "constant", probably about 9.8 m/sec^2 in your location. For "normal" road tires on a standard surface, the Crr will typically be in the range of .004 to .007; heavy tires on rough roads will tend toward the upper part of that range, racing tires on a good surface will tend toward the bottom part of that range. In this case, let's say the Crr of your tires on that road is right in the middle of that range at .0055, and that the all-inclusive weight of you and your bicycle and all of your equipment is a total of 110 kg. Then the rolling drag will be .0055 * 110 * 9.8 = 5.9 Newtons. For each kg that you decrease the total all-inclusive mass, the rolling drag will decrease by .0055 * 1 * 9.8 = .0539 Newtons.
Power is force * speed, so for constant power output the change in speed due to decreased mass will simply be power/change in force.
So, suppose your "cruising" power was 300 watts, your total mass was 110 kg, your CdA was 0.3 m^2 (which is low for a commuter bike setup), and the Crr was .005. We can then calculate your speed as around 10.9 m/s (or 39.2 km/h). If you were to decrease your mass by 10kg, roughly 10% of your total mass, your speed would increase by about 1%, to 11.0 m/s, or 39.6 km/h.