Hello.
I can program a Python script that does what you need.
The program can be made with graphical interface with a small database for storing URLs. Alternatively, it could be done as a command line script that loads URLs from a text file. Whichever you prefer.
For the tweeting part, I would use Tweepy library for working with Twitter API.
Checking for changes in web pages is a pretty straight forward task, but I'd like to see some examples of these web pages. Depending on what you are trying to achieve, there might be some cases in which you'd want to overlook some changes in web pages.
If you consider me for this job or if you have any questions for me, feel free to contact me anytime.