Of course will the removing of not needed data - either in columns as well as in records - reduce the app-size.
Another important part is to reduce the cardinalitely of the fields - here is a great explanation in regard to timestamps: The-Importance-Of-Being-Distinct. Also an adjusting/removing of the field formatting might reduce the size.
Last but not least has the datamodel a big impact. For example the quite popular link-tables could be grow bigger as the related fact-tables and increasing the app-size significantly.
1. Check for Subset ratio in the master data tables(dimension tables)
The master data table or the dimension tables should not have a higher subset ratio when compared to the transactional table (FACT Table). This means that there are more distinct values in dimension tables in comparison to the FACT table.
There is no point in having master data details for which there are no facts or transactions in the FACT table.
2. Dropping unnecessary fields should help since it reduces the amount of data being saved. It should also depend on the number of distinct values inside the field/fields that you are dropping
3.There is an option to save the document in high compression. This will result in a smaller file size, but will result in increase in time while opening.
4. You could further check on the level of granularity of transaction table/FACT table in the data model. If in the UI, data is not shown in a very granular manner there is no point in maintaining high level granularity. Use a group by and aggregation to reduce the amount of rows.
5. Go through document properties and look if there are any hidden sheets which are not being used anymore and can be deleted.
6. Go through sheet properties and check if there are any hidden objects/charts which are not being used anymore and can be deleted.
Alternatively you could use QlikView Document Analyzer to understand what all can be removed from the app!