Please call your doctor about watering down her formula, this can be dangerous in babies this young. I'm sorry I don't have any advice to give you because I didn't have this problem, but I do know that water can be dangerous, so I wanted to make sure you knew that. Same with the Karo syrup. My doctor was adamant that we never give it to infants. I would always check with my pediatrician about something like this in addition to getting other mom's advice.
Edit*
All I said was to please check with your doctor about doing something that I had been told by my doctor NOT to do, in no uncertain terms. Yes, you will hear lots of differing opinions when you post on here, that is the great thing about it. I just wanted to give you the same information I was told to hopefully encourage you to get a doctor's opinion as well. I see *opinions* on here all the time that are expressed as fact, when actually, I and other mothers have heard the exact opposite.
So to answer your question- water can be toxic in young babies if they have too much of it. Actually it can be toxic to anyone in very large quantities. But what counts as a large quantity in a 4 week old is a lot different than a large quantity for an adult. It is called water intoxication. I have absolutely no idea what quantity would be harmful to an infant, but I bet your doctor does. All I know is my doctor cautioned me against giving water at a young age. Also, if you dilute the formula too much the baby doesn't get the nutrition they need. Again, a doctor would know what is "too much".
As for the Karo syrup, it is not intended to be a remedy for constipation in infants. It can cause diarrhea. I'm sure some doctors suggest using it, yours did. But mine did not. If I was going to administer this I would want to make sure I had the dosage right, and I wouldn't trust that info from anyone but a doctor. Since you didn't say in your question that you had asked your doctor, I was just suggesting that you do.