Weight loss can have an impact on the appearance of a tattoo, depending on the location of the tattoo and how much weight is lost. Loosing a moderate amount of weight, up to 100 pounds, should not have a drastic impact on a bicep tattoo. This is especially true if you are loosing weight at a normal pace, around one to two pounds per week. By loosing weight at a slow and steady pace, the body has time to adjust and there should not be any noticeable difference in the tattoo.
One major exception to the rules about weight loss and tattoos is weight reduction surgery. Very rapid weight loss, such as what is seen after surgical treatments for obesity, can cause sagging skin all over the body, which can easily affect a tattoo. Barring very fast weight loss, a tattoo on your bicep should look the same before and after loosing the weight.