I can provide the math and the physics:

For accelerating, if the extra weight is at the edge (like it is with tires), the extra weight counts as a factor of two. But as you point out, that changes a 0.5% effect to a 1% effect and that's what it really is. On hills, the extra weight is only a factor of 1, so adding 1 lbs of tires is the same as eatting that 16 oz steak for lunch (except that the tires won't make you feel bad ).

So weight isn't a big deal.

What is a big deal is tire composition. Changing from a racing tire to a flat prevention tire can add a lot of rolling resistance and that you'll definitely notice.

As I just posted in another similar thread, the heavier tires will have more angular momentum and it's possible (but I can't confirm or deny) that you'll feel that when sprinting hard and wobbling the bike back and forth. So it's possible this is what people mean when they say that heavy tires feel "heavier."

Cheers,
Charles