Wow, I must have been tired when I posted. You wanted to know if the Thief was balanced, and I'm giving you a Thief guide, lol. Let me try and rectify that.
So yeah, the single classed Thief does go up levels quickly, but with the second-worst Hit Die and Thac0 progression, as well as a fairly lackluster saving throw progression (I mean look at that Breath Weapon save- sure Thieves can get their Defensive Adjustment from Dexterity added to that, but so can everyone else, and this is something you'd expect Thieves to be good at!).
The issue becomes what is a Thief supposed to be doing inside of combat- his utility outside of combat will eventually become pretty good, but at low levels, few, if any, of his Thieving Abilities are especially reliable.
He is too fragile for melee combat, and Backstab is very tricky to pull off- either he goes in alone and tries to assassinate a target, then has to survive for his friends to back him up, or, as cavetroll suggests, he finds a Ring of Invisibility at a low level (even Tolkien balanced his game this way!).
As a ranged attacker he is also lackluster, and at 10th level he gains the ability to use scrolls...more or less. In his "Gord the Rogue" novels, Gary allowed his main character, a Human Thief, to gain "weapon training" in the long sword, for a +1 to hit and damage, which brought his combat ability roughly in line with a Cleric; I remember seeing a Kit for Thieves, I think from Al-Qadim, that offered a Rogue Weapon Specialization. I think allowing that to Thieves as a baseline might not be bad; just not at 1st level. Allow it when they get their next weapon proficiency slot (I believe at 4th level). +1 to hit, +2 to damage, and the increased attack rate might be decent for a Rogue.
But this still presents the issue of survival- the Thief's hit points might not be as bad, as he's nearly level 3 when a Fighter is level 2, but eventually he will fall behind. The larger issue is his AC, as while he can wear heavier armor, the penalties to his thieving abilities are too restrictive, and the bonuses for wearing no armor at all are pretty tempting! The noise generated by +1 more AC is sufficient to reduce Move Silently by 20%, which I find ridiculous (especially in light of the Ranger). In light of this, I would remove the penalties to Thieving Abilities for Studded Leather Armor (and reduce the penalties for Elven chain by 5% across the board), and give Thieves the ability to use at least a buckler or small shield.