Hello,

This is Justin with Microsoft Office 365 SharePoint Support. 

I apologize but unfortunately the issue you have described will be local and should not be exclusively caused by a specific function such as using the Web Apps.  Perhaps the browser will require more disk activity when loading certain applications such as the Web Apps, however this will require service on the storage devices within the hardware of the machine.

Thanks and Regards,

Justin Ronan
Microsoft Office 365 SharePoint Support