Of course they also effect the sound in indirect ways, namely the difference in playability. For instance lighter strings ease wide bends, vibrato, legato, etc. In addition lower action can be set. Yet at the same time they are more sensitive to fret pressure and prolly won't last as long tone wise (which is already thin as mentioned) and break more.
While heavier ones yield sustain, warm tone, and that full sound. But that comes with slightly higher action or more fret buzz...and dead notes if you don't mash 'em down with strength.

After most shifts in gauges a quick set-up tweak is needed for action and maybe intonation for them to work best. Putting on some heavies tuned lower for the slackness may be what works for you. In the end, like most things, it's a preference or like an acquired taste.