MySQL modifying order by rand() to other methods

I am now trying to make random selections from each grouped column array, with chances followed by the weight of each row. For example, I have a table (DemoTable) like this: http://sqlfiddle.com/#!9/23470/3/0

Name	State	Grade	Weight
John	NY	100	1
Liam	NY	90	2
Olivia	NY	90	3
Emma	NY	80	4
James	CA	10	1
Henry	CA	20	1
Mia	NJ	50	1
Ava	NJ	30	4

For State = 'NY', there are four rows with grade array: [100, 90, 90, 80] and the weight [1, 2, 3, 4], respectively. So 80 has the largest chance to be picked while 100 has the least within its State group. I made a query for it:

SELECT a.*,
(SELECT b.Grade FROM DemoTable b WHERE a.State = b.State 
ORDER BY RAND() * -b.Weight LIMIT 1) AS 'random_val' FROM DemoTable a;

and it worked with the result:

Name	State	Grade	Weight	random_val
John	NY	100	1	80
Liam	NY	90	2	80
Olivia	NY	90	3	80
Emma	NY	80	4	90
James	CA	10	1	20
Henry	CA	20	1	10
Mia	NJ	50	1	30
Ava	NJ	30	4	30

Though, I would like to know if there is any other method like join or union instead of using order by rand() alone.
Is there any other way to modify my MySQL query that gives the same result?
I would sincerely appreciate if I could get some advice.