In 我三岁了, 了 can be construed as either *the state of change* or *completion(already)* according to contexts. 

E.g. 

> A: 你几岁了
>
> B: 我三岁了

In this case, B simply means I'm three years old already. He doesn't indicate the change 2->3. He just tries to tell the truth that he is being 3 years old now. 

Another example, say today is your birthday, you can say 我三岁了 to indicate that now you have reached 3. In this case, the change 2->3 is implied. 

***I might think the-state-change 了 only works well for present***. It doesn't work well for past and future. E.g. 下雨了，成功了，我们胜利了，etc. I would prefer not to use 了 in the sentences like 我明年三岁了 and 我去年三岁了. I might as well say 我明年三岁 and 我去年三岁. 

I think the reason why the-state-change 了 works well for the present is that it can add some effect of *exciting, surprise, joyfulness, happiness, etc.*. Using it in the past or future, people won't feel the effect. Thus, ***it becomes redundant there!*** 

If you want to emphasize the change in the future or past, we can add 就 for effect. E.g. 我明年就三岁了，我去年就三岁了. Without 就, the effect would be lost. 

My two cents.