The Messange: Could not execute SQL: CREATE DATABASE "NewProjectName", means that you are trying to create a new database "NewProjectName" and do not have permission to do so. 
To create a new Project in ShipWeight you have to do following:
Create a new project by clicking "new project" on the toolbar in the Main Window, or by selecting Project | New in the toolbar menu in the Main WIndow.
In the Project Info Window that now appears you have to select one of the existing databases in the DatabaseID field, and then you can write the name of the project you would like to create in the Project ID field. Fill in the project information and click ok. Now you have created a new project with the name "NewProjectName".