How is the size of a video related to its perceived quality?
At least for images (I don't know of such a result tested on videos) for a given resolution, there is an optimal display size (assuming constant viewing distance. otherwise, display size should be measured in angles from the viewers point of view). In a paper from 1989, Peter Barten provided a formula to compute this effect [1]. The gist can be seen in the following figure from that paper: 



For the low resolution images (e.g 100px wide) there is a slight advantage in quality ranking for the smaller screen over larger ones. However, as the number of pixels increases, the perceived quality on the small screen saturates, and larger screen are preferred.



[1]  The Effects of Picture Size and Definition on Perceived Image Quality. Barten, P. G. J; IEEE Trans.on Electron Devices, 36 (9), p. 1865-9, Sept.1989
doi: 10.1109/16.34260