Really, I'm not really seeing huge issues. Understandably large characters may not be to everybody's taste (much like tiny characters), but I don't think they'd be intrinsically broken.
I don't think there are -insurmountable- issues, particularly in a home game. But I do think there are significant issues that one needs to take into account to be fair to other players.
Larger footprint
For: Easier to block enemy movement, more likely to trigger OA against enemies, burst attacks made a lot larger
Against: Easier to get slowed down by difficult terrain, more available spaces for enemies to attack from, less room for allies to manoeuvre.
Seems fairly balanced, apart from the bursts. Use mounted rules, and it works, in my opinion.
I wouldn't use mounted rules, actually. Let the large character get the benefit; it's mostly balanced, particularly if you consider it one of their racial features.
Note that also in here is (separate from reach) the ability to hit creatures 10 feet off the ground). The vertical height is certainly an advantage, but again, almost balanced by limited maneuvering ability.
Larger weapons
For: Deal +1 die-step for most weapons e.g. 1d8>1d10
Against: Difficulty obtaining large weapons.
Now that's a flat bonus. But really, all it equates to (very roughly) is a +2 melee damage bonus, right? Doesn't sound so huge to me.
It's huge. It's not +2 damage with melee, it's +1 damage--but that's at least +1 damage per die, and +2 on a crit. So the paladin with a +4W daily starts dealing out +4 damage on that daily at first level, and the ranger is dealing out an extra two damage (at least) per turn. unbalancing that PC WRT other PCs. Worse, the brutal rules break when you start messing with weapon dice; while most weapons go up by 1 damage, for instance, an Executioner's Axe goes from brutal 2 1d12 (average of 7.5 damage) to brutal 2 2d6 (average of 9)--so a paladin with an EA starts doing an extra 6 damage on her 4W daily, which certainly makes a difference.
I'd want to balance this out with something similarly large. Probably -1 to AC.
Obviously, the Centaur doesn't suffer from this, which was why it was a fantastic idea.
Reach
For: Hit enemies from 1 square further away. However, no threatening reach.
Against: Nothing really.
I think reach is a pretty big deal, even without threatening reach.
However, not all large creatures have reach - and I don't think it would be breaking things too much to say that large races that traditionally have it don't when made into player races (such as an ogre).
Easiest approach is just not to give reach, yeah. Certainly not threatening reach -- or at least if you want threatening reach, you want to be -really- careful (and at that point you're talking tentacular; mostly if it doesn't have tentacles, it doesn't have threatening reach). Reach is a big deal, of course, but it's easy to overrate, given that it's easy enough to get via magic items and that more monsters have it as things grow larger, plus that reach weapons don't necessarily do -that- much more damage than non-reach weapons. Not worth that much thought, though.