1000 kg is just over 2 lbs. Now it depends on the rest of the system. If it's me, with my bike, and my pannier for work, that's well over 250 lbs, so even 2 lbs is less than 1 % and I'm not going to notice that.

For tires, here's my point: What almost everybody is actually talking about when they say heavy tires feel slow is that fast rolling (but not flat resistant and not durable) tires roll a lot more poorly than slow rolling (but more durable and flat resistant) tires.

Again, if you don't believe this and want to verify it for yourself, carefully add weights to the end of your spokes. Make sure that the wheel still rotates evenly, then you can add weight and not change the rolling resistance, so we can actually measure the one effect at a time.

Cheers,
Charles