Sounds like you have an aggressive competitor. Survival of the fittest is how you keep your head above water. He/She is doing to you, what you should be doing to them in reality.
Your competition wants to take business away from you so they can grow their client base. You need to focus on what your customers need and offer the most comparable services and prices. Either that means you offer the same price for the same service or better price for the same service. If you can't afford it, offer the same price with better service or tack on something for free that your competition doesn't have.
But be ready, because it sounds like they are watching you and might counter your offers. Regardless, don't lose focus on what is most important. Your customers.
When it comes down to the nitty-gritty, it's not really about removing weaknesses, it's providing the service that your customer wants and feels most comfortable going to. You will have a large pool of customers that will go for the cheapest/easiest service, but you will also have the other half of customers that are willing to pay a little more, for that feeling that they are more than just a source of money for you.
Look at it this way. Why would you want to pay $32 dollars for a cheeseburger at a fine dining restaurant if you can go to McDonald's and get one for $4 bucks?! You might be the customer that only has $4, but you complain about the horrible service you got and refuse to go back to that place. You might also take your date out to a nice place that treats you like royalty and have a great time, great meal, and great service. And even though you spent a lot more, you and your date agree that you would like to go back again for another date.
So think about the standards and service you want to offer to your customer, what kind of image do you want them to have of you? Are you also just a standardized business that is more cookie cutter like, or do you stand out from your competition?
Hope that helps, Good luck!