you could limit the character's eye rays to those magical effect that a caster of the same level would be able to cast, in addition to the penalties given by the "negative levels"

so at equivalent party level 3 he would have access to 1st and 2nd level rays (sleep, charm person, inflict moderate), at level 5 he gets access to slow and fear, at 7th charm monster, at 9th telekinesis, at 11th flesh to stone and disintegrate, and finally at level 13 he's a full beholder with no penalties and access to finger of death.

maybe make it so that the telekinesis eye works as a kind of mage hand before 9th level, unless you find the constant subplot of "how am i going to open this door" to be extremely fun :D

You could similarly let the antimagic beam "power up" with levels: at 3rd level it's completely offline, at 5th level forces spellcasters in the area to roll a caster level check in order to be able to cast with a DC of 10+the beholder caster level (basing it on dispel magic here), and either at 11th or at 13th level it graduates to the full anti-magic cone

As a way to distinguish his character from the other beholder who do not go around adventuring, you could give him the option to personalize a few of the eye rays he gets by leveling up, by choosing other effects of comparable level.