There is no need to balance, but you may want to control it anyways
The wizard class description is designed for wizards to be balanced, even if they eventually have access to their entire spell list. Quoth the PHB:
On your Adventures, you might find other Spells that you can add to your Spellbook.
The reason for it is that one of the major limitations as a wizard is how many different spells you can prepare in a day. After you prepare all the generally useful spells like those listed below under "bread and butter", you typically have preciously few "free" preparation slots left. It does not matter if you have a spellbook of dozens other spells then. I speak from practical experience: I have copied several spells to my book that in the course of seven levels worth of play that I have never even once used; and that even though I make it a point to prepare such subpar spells on purpose, to see if I can find some fun, creative application.
Copying Spells is costly
In addition, I agree with @Jack that often it may be difficult to transcribe all the spells you find for time and cash reasons. I know that I have struggled with that for many levels in a relatively fast paced campaign, where the other players' characters have no reason to hang back at home for days on end. The money is also always too short and I am in debt. I think it is a valid reason why handing out spells liberally at some point yields diminishing returns to the player character wizard. But Jack made this point much more eloquently already.
Even if the time constraint is absent and your campaign has liberal downtime days, the cost constraint remains. (Note that having no urgency would be a balance issue: 5e is balanced for 5 encounters a day. If nothing is pushing the group to press on, they can long rest after each encounter, breaking game balance).
Quantitatively: to learn all the spells from the core rules up to 3rd level (after your picks at caster level 6) would cost you nearly 8,000 gp. Your expected wealth by then is about 4,500 gp. You'll not be able to afford it. (As gold grows quicker than spells, you will catch up around level 8, but this does not even factor in costly components you need, like a crytal ball for 1,000 gp, or a Leo's chest Replica for 5,050 gp).
For both these reasons, I personally think there is no balance issue.
Limit it anyways
However, I still would be somewhat stingy in handing out good additional spells: the longing for that which they do not yet have is a great driver for engagement by the players, and finally finding a long-sought spell is a great reward. So don't go monty haul. Make it meaningful for the wizard to find the great spells. The following methods can help you do so:
Wizards hide their spell books
Wizards are really scared to lose their spell books. That is why it is common that, once they have learned the selection of spells they like, they hide their books in a safe place. In this case, the wizard will not have the book on his person, and finding it becomes a challenge in itself. Spellbooks are not magical items either, so they are not easy to detect through floor tiles and such. Clever wizards may even use decoy books to foil things like Locate Object. There are many published adventures where the spellbooks are cleverly hidden somewhere. Have your wizards do so, too.
Limit the amount of novel spells
Granted, not all wizards should have the exact same spell list. But many spells are bread and butter for a wizard and will likely be shared, think Detect Magic, Armor, Shield, Magic Missile, Invisibility, Misty Step, Counterspell, Dispel Magic, Haste, Fly, Fireball and/or Lightning Bolt, Sending, Polymorph. If your red wizards share a core of common spells, the number of extra, novel spells that reflect each wizard's specialty can be kept small, maybe one or two spells per book. This will make players happy (and can be reflected by accounting for it in the overall treasure calculation), upholds believability, and limits what you effectively hand out.
Add subpar spells
This is of course subjective and likely worth a discussion for each case, but there are a lot of spells that are not that desirable, because they are rarely applicable, or they have effects that are in many regards inferior to a similar spell.
By providing such spells as the extra spells, you can keep the spellbooks varied while at the same time not granting much power to the wizard. Some spells I can suggest (although other's opinion may differ, and they surely have some value in special circumstances): Illusory Script, Jump, Ray of Sickness, Witch Bolt, Darkness, Darkvision, Nystul's Magic Aura, Bestow Curse, Feign Death, Vampiric Touch, Elemental Bane, Blight, Phantasmal Killer, Seeming, Move Earth, Symbol, Control Weather
Add redundant spells
There also are spells that have largely similar effects. While they may add slightly to the versatility of the PC wizard, the benefit will be mild. For example, instead of Fireball they could learn Lightning Bolt or Vitriolic Sphere, and while that may be of use in an adventure against fire-resistant enemies, in many cases they substitute for each other as mid-level area damage spells.
Spellbooks may be hard to sell
Even if they are not magic items, spellbooks are only useful to wizards. There may not be a market to sell spellbooks easily, especially when in contrast to scrolls, it also costs a lot of money to copy them into a form you can use (50 gp in inks per spell level plus an empty spellbook on top). You as the GM can rule that it is as difficult to offload a spellbook as it is with a magic item, so their monetary value is questionable. Furthermore, merchants may not want to buy a spellbook that is clearly one of the red wizards', for fear of being targeted for retribution from that group.