Well, yes, it is possible for your eyes to change color with weather. Generally speaking, there are many factors which can lead the eye color changes. For example, your eye color can be changed with the weather, emotion. Your eye color can change due to the weather. For example when it is really sunny outside and the sunlight hits your eyes, it can cause your eye color to become brighter. Also, when you are sad, concerned, worried, and have cried, the color of your eyes will become light grey and light blue. By the way, color change in your eyes is caused by blood pressure. So when you are clam, your eyes' color can change to grey. For the weather, your eye color can change. And you should not be too worried about it.
Actually the eye color do not directly changes with the weather. But it does have some connection.What does change is the way light reflects off the iris, creating the impression that the color of the eye has changed. To understand this phenomena, look at the factors that contribute to eye color and affect the quality of light reflected.
So ,you can see that if the eye color may be slightly different between rainy day and sunny day.
No, it is not possible for the eyes to change the color with the weather. The color of eyes is fixed according to the genetic endowment when you are a child. Thus, it will not change with the weather. When you find the eyes change the color, you'd better go to see the doctor and have a check on the eyes.