i agree that its more of a problem on weekends. i assume its cause more players on that are casual (kids that have school, or adults that work week days) and just dont care.
i do hope that the reporting system is weeding these people out, (which isn't reallly super effective, with no anti-smurfing enforced, if they get banned they just make a new account). and do hope riot keeps up/ramps up bans on this.
but, that aside, since its out of my control. i found it improves my game to keep my head straight. and in particular on this situation, that, for me, means accepting before matches on weekends that this happens more, and by accepting it, i find myself tilted less.
before that, my approach was play past 4am. but... that seems to not work, as theres a lot of non NA people playing on NA during those hours either farming accounts up in lvl to sell, or simply messing about. all of which have very high ping, so die a lot, or dcd and afk a lot.