You have two balloons. Lets say you have a large balloon and let out a certain amount of air and the balloon decreses by 10%. Now you have a small balloon and let out the same amount of air and the balloon decreases by 50%.

Lets say someone overweight and with a large belly looses 12 pounds this may not be noticeable. But the if that same person lost more weight and had an average build and then lost a further 12 pounds it will have more of impact.

Basically, if someone loses exactly 1lb a week will the weight loss be more noticeable as the person grows thinner?

oh wow it took me three readings to understand that
to be honest the overweight u are even the slightest weight loss shows..as compared to the thinner version(my personal experience)
when i lost first 10 lbs everyone noticed and wheni lost the last 10 i had to tell everyone that i lost yet another 10 lbs.

Theoretically I would agree with the OP. It stands to reason that if a 250lb person loses 12lbs it would be less noticeable than if a 125lb person were to lose the same amount.

However, as with many things related to weight loss, the theory doesn't always prove to be the case in reality. People store and lose bodyfat in very unique ways and no two people will lose weight from the same places at the same rate, even if their weight and rate of fat loss is the same.

It really depends if where you lose the fat from and whether it is noticeable to other people. Assuming that we don't all walk round naked all the time, there are only limited parts of our bodies on display. For example, if you lose a lot of fat from your facial area, it tends to be noticed by other people whereas if you lose a lot of fat from your torso area and your torso area is covered by baggy clothing, its unlikely as many people will notice.

Another thing to remember (as I am assuming that this relates to your other thread) is that people won't necessarily tell you if they notice a difference. They may feel they don't know you well enough to comment on your appearance or, they may think you'll take it the wrong way (ie. to say you look slimmer is to imply that you were fat before.)

The most important thing is that your progress is noticeable to you.

HTH