Magic items are limited by places on the body to put them so that they fit/stay, and are not too close to one another (which is why you can only have one in each slot, can’t wear ten rings, etc.)
When you have more body parts to put things on, you get to use more items. When you have fewer, you miss out on some items. See Table: Magic Item Slots for Animals for some examples: while none of these have four arms, it clearly shows that different body types have different sets of magic item body slots.
Generally speaking, this isn’t terribly much of an issue, at least in-and-of-itself. The character still needs to find those magic items in the first place, and that is usually a much stricter limitation. Pathfinder does play up the restriction somewhat, at least in the case of physical-ability-enhancing belts, but your character doesn’t have two waists, so that doesn’t come up.1 Getting an extra pair of bracers/gauntlets/gloves is just not that serious.
On the other hand, getting to wield more weapons, or wield a two-hander and a shield, or whatever, whether they’re magical or not, is a pretty big deal. This is why getting more than two arms usually requires massive investment. Assuming your player’s character has paid appropriately for those arms (in terms of race points, feats, class levels, gold, whatever), then this is basically what they were paying for. In my experience, actually, these things are usually overpriced.
- The limitation of physical-ability-enhancement to belts only is also an utterly atrocious idea that should be thrown out by every DM ever, since it’s a brutal shafting of the weakest classes. Please do not force your players to pay premiums on top of their ability taxes.