Actually you can do it without a module - Prestashop already displays colors on product listing, so all we need to do is to change this into sizes.
You need to know ID of your sizes attribute group, having that (example for the classic theme):
1. put the attached Product.php file into override/classes
2. in that file, replace ATTR_GROUP_ID in line 22 with ID of your attribute group responsible for sizes (for example 1)
3. modify \themes\classic\templates\catalog\_partials\variant-links.tpl to show variant name (also see attached file)
4. clear the cache and you should be done 