The standard template that datakick module installs do not contain shipping weight by default.
You can very easily add it, though.
GMC documentation https://support.google.com/merchants/answer/6324503?hl=en tells us that they are looking for element like this
<g:shipping_weight>3 kg</g:shipping_weight>
So let's edit the template, and add this element under <entry> node
To get data in correct format, you need to use the expression
product.packageWeight + " kg"
Note that you need to do this twice if you are using GMC template for combinations, as there are two <entry> nodes in template, one for products without combinations, one for products with combination. In this case, you will need to use different expression in second node:
combination.packageWeight + " kg"
You can download this template: gmc-with-weight.json and install it into your datakick module, as an inspiration