In Layer > Properties > Fields (I think), select an Image edit widget for a field. Select the images you want for each feature, and then run qgis2web. Set that layer's popups to that field or all fields, and export. The images should appear in your popups.
Try to make the images a suitable size, and do report any issues on Github. I'll release a new version including this functionality early next week, once I've updated the readme.
It looks like there was a regression in qgis2web for OpenLayers 3 raster layers. I've committed a fix to the Github master branch at https://github.com/tomchadwin/qgis2web. Please try that and leave a comment to this answer to say whether it fixes the problem or not.
Best Answer
Please download the current master branch of qgis2web from Github:
https://github.com/tomchadwin/qgis2web
In
Layer > Properties > Fields(I think), select anImageedit widget for a field. Select the images you want for each feature, and then run qgis2web. Set that layer's popups to that field or all fields, and export. The images should appear in your popups.Try to make the images a suitable size, and do report any issues on Github. I'll release a new version including this functionality early next week, once I've updated the readme.