Changes to airline tickets normally include 2 components :
1) A 'Change Fee', which is as the name implies a change to actually make the fee. The actual fee will vary depending on a number of factors including the type of fare you have, when you purchased it, where the flight is to/from/etc. In general, change fees range from $0 up to $500 or more - but normally are in the $100-$300 range.
2) A 'Fare Difference'. Fares vary based on a number of factors, including day of week, time of the year, how long you stay at your destination, how full the plane is, etc. When you change flights to a different day, the fare is re-calculated for the new date, and as a result it can vary significantly.
In your situation I suspect the majority of the difference is coming from the 2nd item. For some reason, the fares available for your new dates are more expensive than your original dates. This could be as simple as them being on a different (more expensive) day of the week. It could be because your original fare was deeply discounted, and that fare had date or length of stay restrictions that you're now going beyond. Or it could be any number of other factors.
In order to try and reduce the fee, check online to try and find days when flights between the two locations you're flying are cheaper - just like you would when booking a new ticket. If/when you find cheaper days, then contact the airline and see how much it would be to change your flights to those same day(s) and I suspect you'll find the price will drop from what you've originally been told.
You could also ask the airline to see if there are any restrictions in the fare rules for your current fare that will be relevant. eg, if the fare has a maximum 30 day stay and you're now going over that then this will almost certainly result in a fare change to move to a less restrictive fare class.