NOTE: If you want to update the weight of just one product, there is an existing support document for this. 

Firstly, you will need to update your Magento CSV with the new weights of the products.
To download and access your Magento CSV, a detailed explanation can be found on step 3 of this support document.

Next you will need to login to your Magento Admin Panel.

From here we need to access the Import/Export Product page. To do this, click 'System' on the navigation bar, then hover over 'Import/Export'. and then click 'Dataflow - Profiles'.

To be able to upload the CSV, select 'Import All Products'.

Then under the 'Upload File' tab on the left, click the 'Choose file' button and then browse to your CSV file on your computer.

Then click 'Save and Continue Edit'.

The final step is to select the 'Run Profile' tab on the left, and then 'Run Profile In Popup'.

This will then open a screen which looks similar to the one below. Once you see 'Finished profile execution', it means the CSV has successfully uploaded to your Magento store.

The new weights will be added to your products on Magento.

If you need any help with this, or any other problem, please contact our support team.