I actually have 5 UA Shortsleeve T Tops, they were all bought at different times at my local sporting goods store, except the last one I got on Amazon since I wanted to have a different color.

The shirt is a semi- & dry fitted shirt, not too tight and not too baggy, true to its size, and it's light in weight.  When you sweat, you won't feel like the shirt is saturated with sweat (feeling heavy).  I wear them during my kickbox cardio classes at the gym, and I can definitely see my sweat under my both arms and chest area of the shirt (the reason why I mentioned is because another reviewer stated that the sweat is not visible on the shirt), maybe I sweat a lot during the excise, but it does not bother me at all since it's normal to see people have sweaty spots on their shirts in the gym.  On the other hand, the shirts do dry quickly once I step outside of the gym; so if one is to wear this shirt for running, I do not think she will need to be concerned about sweaty spots on the shirt.