When you lose a significant amount of weight in a short period of time, this may influence an already existing tattoo. If the weight loss only entails a couple of kilo's, your tattoo will most likely look the same. However, when you lose 20 kilos for example, it is not unusual for your tattoo to be affected.
Certain body parts will be more susceptible than others. Tattoos on hands and feet will hardly show any changes but ink on the belly, arms and upper legs can look less attractive because weight loss can cause excess skin.
If there is weight gain, there's a chance your tattoo will stretch out along with your skin. This can cause colors and lines to fade. In this case a 'touch-up' can be a solution. This also depends on the size and location of your tattoo. A large portrait is more easily affected than say, a small modest letter or sign.
So make sure to think carefully before you decide to get a tattoo when you plan on losing or gaining (a significant amount of) weight. It is almost always advisable to get the tattoo when you've reached your ideal weight.