I know to use it once a week. Will it get stronger each week with repeated use or is the way my hair feels after using it once the best it's going to get?
You can over do it. Well, some can, not everyone. I have to be careful as my hair can go brittle quite quickly. Others seem to be able to use it to their hearts content and it makes their hair feel lovely every time.
It just depends. One application a month is all the added protein some people's hair can handle, some people can use it every week, etc. So every time you use it, you're adding more protein/strength to the hair, but like Janine said, there is such a thing as over proteining the hair, which can be just as bad if not worse than not having enough protein. The hair can become brittle and crunchy/hard feeling and in some more extreme cases it can break right off. Most people can usually do 1/2 protein treatments a month and have a nice healthy level of protein in their hair. A lot of times the hair will feel dry after a protein treatment which is normal, so most people do a deep conditioning treatment afterwards, as hair needs a balance of moisture to protein.
I only use it once every 10 to 15 days as my hair goes brittle with too much use. Its a trial and error thing. You just have to test it out until you find the best way for you.