What would be the first aftermarket part I should buy?

The advantage was you accelerated at a faster rate being lighter so you will pull ahead and keep that lead even if both of you eventually arrive at the same speed.
 
Indeed, blue has a good point. If the race is based on arriving at the end of the street, not on the top speed of the bike.
But even then you have tyres sized and inflated for your weight. Your friend has tyres sized and inflated for his weight. You swap bikes and you both have the wrong size and/or pressure in the tyres. One overinflated and one underinflated. Having underinflated tyres is worse for your rolling resistance than having overinflated tyres especially on smooth paved road.
 
One trick at the drag strip was to over inflate the front tires to help minimize rolling resistance..of course dropping back down to recommended pressure afterwards for the drive home.:)
 
we thought of that and just did a rolling start at his best speed, after which I just pulled away at greater speed than he could manage

no need to discuss it, just find a friend that is 40 or 50 pounds different in weight from you and try it (or even just have a car pace each of you on same bike to see top speed)
 
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