I know that がち means "tend to..", while 気味 means "to have the feeling, to be a little..". Like 病気がち, tend to get sick, and 風邪気味, have / feeling like having a slight cold. But how about this: この時計は遅れ気味だ. Does it means the clock is a little late? Because if the clock tends to be late, it should be この時計は遅れがち, right? Thank you!
Both sentences are correct, but have different meanings.
この時計は遅れ気味だ simply means the clock is currently a little slow. You can just adjust it to the correct time, and the problem is solved. But depending on the context, I feel it may mean the same thing as 遅れがちだ described below.
この時計は遅れがちだ only means the clock tends to be slow, i.e., even after adjusting it. Perhaps you need to replace a battery, or you want to buy a new clock.
Apparently you already know why.
"この時計は遅れ気味だ" just means the static situation that this clock is slighty slow. So once you correct it, probably it'll work properly.
"この時計は遅れがちだ" means the clock tends to be slow, because of the internal problem of the clock. So if you correct it, it'll slow again.