There's no need for rules light; there is need for straightforward rules that resolve quickly. Different things. Rules medium with low rolling can and often does work fine.
It also helps a lot if players know what the dice needed are going to be in advance, and that difficulty doesn't affect the numbers, types, nor modifiers to, the dice themselves.
Games I've run for 9p+ groups: WFRP 1E, WEG Star Wars, my own homebrew Trek game (12p campaign, 2 PCs per.).
other Games into the 7 or 8p I've run: AD&D2*, Advanced Marvel Super Heroes (TSR), Legend of the Five Rings 5th (starts to break at 8; I've had a couple 10p sessions), Ars Magica (8p campaign), FASA Star Trek Role Playing Game (both eds) (7p), The One Ring (7p), MegaTraveller (7p), Mouse Guard (7p), Star Trek Adventures (8p con session), Talisman Adventures (7p campaign), Tunnels and Trolls 5th edition (from 1979! 8p 1-shot)
Games I've been in a player of with 7+, but not run large parties: Star Frontiers, AD&D1e*, Palladium Fantasy RPG.
Of that list the ones I'd not use? AD&D (either), Ars Magica (because it works best with deep character investment, my own Trek game as it is too detailed, FASA Trek (lack of utility in certain roles). Palladium, simply because it lacks social rules.
Ones with minor issues to be aware of in large group play:
The One Ring - the hope pool can result in issues due to discussions over whether or not the draw will result in shadow... (technically, each draw requires support of half the party or it generates a point of shadow), and the combat conceptually takes a couple sessions to set in.
MegaTraveller: keeping track of who has gone in combat. Modifiers to rolls.
Mouse guard: you need to increase the number of GM turn encounters above 4p, I added a duplicate per 2 players over, I'd actually suggest 1 per player over... but it also lengthen's the session proportionally, and at 5, you have to have two teams in conflict. Luke Crane said I was crazy... but it ran beautifully for a 7p mini-campaign.
Tunnels and Trolls: it helps to have a good calculator to hand. I'd use 7.5 or Deluxe these days, but the core is still the same.
Major issues:
Advanced Dungeons and Dragons (both): combat can strongly suffer from analysis paralysis (spellcasters), and it only works well in large groups when the GM trims back the rules a good bit. Given that I refuse to run either ed again... I can't recommend it.
Ars Magica: for a short run, not so good. lots of paperwork in the intended playstyle.