Hi Nazia,
In Geographically Weighted Regression, the explanatory variables can be categorical. As long as your dependent variable is continuous, it is fine to use categorical variables as explanatory variables. However, to use a categorical variable appropriately, you can't just assign values 1 through 8 to it. As you found, GWR will try to use these actual numbers, and you will get very different results depending on which levels you label as 1 through 8. For GWR to work properly with your categorical variable, you need to convert it to several indicator variables (variables that have the value 0 or 1) and then use these indicator variables as explanatory variables in GWR.
The process of converting categorical variables to indicator variables is called "dummy encoding." Here is a good article about how to perform dummy encoding:
Dummy variable (statistics) - Wikiversity
In your case, your categorical variable has 8 levels, so you will need to make 7 indicator variables to represent the different levels (you always use one less indicator variable than the number of levels of the category).
You'll need to make 7 new fields on your feature class. For the first field, each feature that is in the first level of the category gets the value 1, and features in any other level get the value 0 (we say that the 1 "indicates" that the feature is in that level). Similarly, in the second field, the features of the second level get a 1, and all other features get a 0. Same for levels 3 through 7. For level 8, the value 0 should go in all 7 fields.
When you encode this way, it does not matter which levels of the category is called the first, second, etc level of the category. Changing the order will produce the same results in GWR.
Please let me know if you have any other questions or have any problems encoding your variable.
-Eric Krause