Assigning extra information to all database table fields

I'm an experienced desktop app programmer, but fairly new to database programming. I'm working with C#/SQL right now. I understand the concept of a lookup table, as in storing a two-character state (such as CA) in a field in one table, and then being able to get the full state name (such as California) from a second table:

Table: Address
AddressID int <PK>
StateCode char(2) <FK>
...

Table: State
StateCode char(2) <PK>
StateName varchar(25)

My question: is there some similar way to be able to provide just about every field of every table with a means of holding common, extra information? For instance, let's say I wanted to store, say, an extended name and some special code with every field in three tables. As in this simplistic example:

Table: A
Field1 int
Field2 varchar(20)

Table: B
Field1 bit
Field2 int

Table: C
Field1 int

Table: ExtraInfo
LongName varchar(50)
TypeCode int

If I wanted to be able to have the information in the ExtraInfo table associated with each field in Table A, Table B and Table C, how would I do that?

Thanks!