If I on one ride add 1 kg of weight to the bike, how much slower (in time) will I be?

Assuming that you and your bike mass 100kg (in round numbers), an extra 1kg causes a 1% increase in weight, i.e. a 1% increase in the potential energy associated with climbing the hill.

If your power output is constant, that implies a 1% increase in time.

However some of your power output is going to overcome wind and rolling resistance, not potential energy. If only half of your power is going to potential energy (which depends on weight), and half is constant (independent of weight), I think that would imply a 0.5% increase in time.

Does that make sense, I don't think so without saying how many watt I output, lets say I make 250W

What I wrote above is unaffected by your total power; the change is relative rather than absolute: i.e. it's 1%, no matter what it's 1% of.

Part of the hand-waving in my statement is "If your power output is constant": which is true if you have fine control over your gears (so that you can, like, you know, gear down by 1% in order to adjust to the 1% increase in the weight-and-therefore-effort).

The change isn't actually linear: for example if it were a 1000kg increase in weight, i.e. 10000% instead of 1%, you'd need to gear down so far that you'd be going so slowly that you couldn't stay upright on a two-wheeled bike. For relatively small increases in weight, though, I expect the difference in effort (and therefore also, via the hand-waving outlined above, the difference in the duration) to be approximately linear.

If I on one ride add 1 kg of weight to the bike, how much slower (in time) will I be?

Assuming that you and your bike mass 100kg (in round numbers), an extra 1kg causes a 1% increase in weight, i.e. a 1% increase in the potential energy associated with climbing the hill.

If your power output is constant, that implies a 1% increase in time.

However some of your power output is going to overcome wind and rolling resistance, not potential energy. If only half of your power is going to potential energy (which depends on weight), and half is constant (independent of weight), I think that would imply a 0.5% increase in time.

Does that make sense, I don't think so without saying how many watt I output, lets say I make 250W

What I wrote above is unaffected by your total power; the change is relative rather than absolute: i.e. it's 1%, no matter what it's 1% of.

Part of the hand-waving in my statement is "If your power output is constant": which is true if you have fine control over your gears (so that you can, like, you know, gear down by 1% in order to adjust to the 1% increase in the weight-and-therefore-effort).

The change isn't actually linear: for example if it were a 1000kg increase in weight, i.e. 1000% instead of 1%, you'd need to gear down so far that you'd be going so slowly that you couldn't stay upright on a two-wheeled bike. For relatively small increases in weight, though, I expect the difference in effort (and therefore also, via the hand-waving outlined above, the difference in the duration) to be approximately linear.

If I on one ride add 1 kg of weight to the bike, how much slower (in time) will I be?

Assuming that you and your bike mass 100kg (in round numbers), an extra 1kg causes a 1% increase in weight, i.e. a 1% increase in the potential energy associated with climbing the hill.

If your power output is constant, that implies a 1% increase in time.

However some of your power output is going to overcome wind and rolling resistance, not potential energy. If only half of your power is going to potential energy (which depends on weight), and half is constant (independent of weight), I think that would imply a 0.5% increase in time.

If I on one ride add 1 kg of weight to the bike, how much slower (in time) will I be?

Assuming that you and your bike mass 100kg (in round numbers), an extra 1kg causes a 1% increase in weight, i.e. a 1% increase in the potential energy associated with climbing the hill.

If your power output is constant, that implies a 1% increase in time.

However some of your power output is going to overcome wind and rolling resistance, not potential energy. If only half of your power is going to potential energy (which depends on weight), and half is constant (independent of weight), I think that would imply a 0.5% increase in time.

Does that make sense, I don't think so without saying how many watt I output, lets say I make 250W

What I wrote above is unaffected by your total power; the change is relative rather than absolute: i.e. it's 1%, no matter what it's 1% of.

Part of the hand-waving in my statement is "If your power output is constant": which is true if you have fine control over your gears (so that you can, like, you know, gear down by 1% in order to adjust to the 1% increase in the weight-and-therefore-effort).

The change isn't actually linear: for example if it were a 1000kg increase in weight, i.e. 10000% instead of 1%, you'd need to gear down so far that you'd be going so slowly that you couldn't stay upright on a two-wheeled bike. For relatively small increases in weight, though, I expect the difference in effort (and therefore also, via the hand-waving outlined above, the difference in the duration) to be approximately linear.