How can I get the actual data size per row in a SQL Server table?

Try this script:

declare @table nvarchar(128)
declare @idcol nvarchar(128)
declare @sql nvarchar(max)

--initialize those two values
set @table = 'YourTable'
set @idcol = 'some id to recognize the row'

set @sql = 'select ' + @idcol +' , (0'

select @sql = @sql + ' + isnull(datalength(' + name + '), 1)' 
        from  sys.columns 
        where object_id = object_id(@table)
        and   is_computed = 0
set @sql = @sql + ') as rowsize from ' + @table + ' order by rowsize desc'

PRINT @sql

exec (@sql)

The rows will be ordered by size, so you can check from top to down.

I liked the above from Jaime. I added some square brackets to handle weird column names.

    declare @table nvarchar(128)
    declare @idcol nvarchar(128)
    declare @sql nvarchar(max)
    
    --initialize those two values
    set @table = 'YourTable'
    set @idcol = 'some id to recognize the row'
    
    set @sql = 'select ' + @idcol +' , (0'
    
    select @sql = @sql + ' + isnull(datalength([' + name + ']), 1)' 
            from sys.columns where object_id = object_id(@table)
    set @sql = @sql + ') as rowsize from ' + @table + ' order by rowsize         desc'
    
    PRINT @sql
    
    exec (@sql)

And I liked the above from Speedcat and extend it to list all Tables with rowcounts and total bytes.

declare @table nvarchar(128)
declare @sql nvarchar(max)
set @sql = ''
DECLARE tableCursor CURSOR FOR  
SELECT name from sys.tables

open tableCursor
fetch next from tableCursor into @table

CREATE TABLE #TempTable( Tablename nvarchar(max), Bytes int, RowCnt int)

WHILE @@FETCH_STATUS = 0  
begin
    set @sql = 'insert into #TempTable (Tablename, Bytes, RowCnt) '
    set @sql = @sql + 'select '''+@table+''' "Table", sum(t.rowsize) "Bytes", count(*) "RowCnt" from (select (0'

    select @sql = @sql + ' + isnull(datalength([' + name + ']), 1) ' 
        from sys.columns where object_id = object_id(@table)
    set @sql = @sql + ') as rowsize from ' + @table + ' ) t '
    exec (@sql)
    FETCH NEXT FROM tableCursor INTO @table  
end

PRINT @sql

CLOSE tableCursor   
DEALLOCATE tableCursor

select * from #TempTable
select sum(bytes) "Sum" from #TempTable

DROP TABLE #TempTable