Since 2018, there is a really lightweight and user-friendly image viewer called qView that can view WebP images. It also has a nice feature to resize the window frame to fit image. It is also free and open source.
You can download the latest version (3.0 at the time of writing, and it's still being actively developed) as a .deb file from the official website or github and install it with
gdebi or your software center.
To install from terminal:
sudo add-apt-repository ppa:jurplel/qview
sudo apt update
sudo apt-get --install-suggests install qview
After you install the .deb file, you also need to install this package: Qt 5 Image Formats addon
sudo apt install qt5-image-formats-plugins
This is because qView is based on Qt5 and even though it supports many common formats by default, it does need this one package to actually view WebP images.
Note: this addon is pre-installed on Lubuntu and Kubuntu (Qt-based DEs, as expected).
Tested on Ubuntu 18.04, 20.04; Lubuntu 19.10, 20.04.