It's really hard for a 1st level character to be balanced against a 3rd level character. Even if the 1st level has all 18s. (i.e. a 96 point buy). Hit points will just be too low. A fighter with 18 Con will have 14 hit points. A 3rd level fighter with 14 Con will have double that (27 hp on average). Even making a 2nd level character balanced against a 3rd level character is hard. The 3rd level feat all by itself is a significant difference.
Equally, a 6th level character would have to have pretty pathetic stats to be balanced against a 3rd level character. You need stats of 13+ to get many key feats, and to cast decent spells, and a character with a point buy of 2 won't be able to manage that. Such characters are unlikely to be fun to play. A low-stat warlock is pretty effective, though.
But if I had to take a stab at it...
First, I'd extend the point buy table:
6 gives -2 points
7 gives -1 points
...
8 to 18 have standard costs
...
19 costs 20 points
20 costs 24 points
21 costs 29 points
22 costs 34 points
23 costs 40 points
24 costs 46 points
Then (using a funky quadratic progression) I'd assign these point values:
CL 1 = 112 points
CL 2 = 50 points
CL 3 = 28 points
CL 4 = 18 points
CL 5 = 12 points
CL 6 = 9 points
A low level monk or paladin might have strong enough abilities to hold his own against a standard 3rd level character. A 6th level character with a few dump stats can have at least have one or two decent (13+) scores, and class abilities would let him match the third level character.
If the characters are going to be leveling up, all these numbers get wonky. At the very least there has to LA adjustments, but even those aren't good enough. The 1st level godling has to have an LA that increases as he goes up levels (starting from +2), while the useless 6th level character has to have a negative LA that gets worse over time. (A 6th level rogue with a 9 point buy might be equal to a 3rd level character, but a 12th level rogue with a 9 point buy is not as good as a 9th level character).
If you find some numbers that are borne up by playtesting, do let us know.