Generally, a CLI is a positive thing. It won't increase your score by itself, but it will help you keep a lower credit utilization rate which will help your score. For some people, CLIs can hurt, but this only occurs in exceptional circumstances.
Some small lenders are sensitive to the total amount of credit available to you. Thus, if you have more than your total annual income in available credit, these lenders might be careful about extending additional credit to you. Most major lenders, however, seem to extend credit to people with multiple times their income in credit. Alternatively, a single lender might be less willing to extend new credit when you have a higher limit with them. If you are near the cap credit they are willing to extend to you, they will usually deny any additional card applications. However, you can always call to recon the denial and offer to transfer limits. Simply put, more credit rarely hurts but in some very limited situations additional credit can hurt.
In your case with a $3000 increase in limit is most likely a very good thing.
