To report weekly project expenses, resources must first be published in the [Timesheets] module, (ensure [Timesheets] is selected on the [Destinations] tab of the Resource record in the [Resources] module).
Expenses can be charged to a project only if the project status is "In progress" (this applies in standard mode; refer to the Keywords & Labels Setup document of the [Projects] module if the project statuses have been customized).