According to Freudís
psychoanalytic theory Richard is an egoweak person because his behavior
is controlled by his drives, consequently the Freudian id, which is proven
for example when he commands to murder his two young nephews without showing
any pangs of conscience.
His superego never really developed which, according to Freud, happens during the childhood.
During his entire childhood the Duke of Gloucester had never had a chance to identify with someone to model his own moral standards on (the Freudian superego).
Since he was young Richardís parental figure changed.
During his first seven years the young boy lived with his older brother George and his sister Margaret at Fotheringhay without seeing their parents often.
In 1459 Richard and Margaret moved to Ludlow but one year later Richard was pulled out of his familiar environment for the third time. The Duchess of York, George and Richard fled to Philip, Duke of Burgundy.
Richard IIIís whole childhood turned out to be like that. Staying at a lot of different places the boy never had a person to relate to. The environment changed several times but for a proper development of the superego a person to whom the child can closely relate to is very important.
Having such a curriculum vitae it does not necessarily mean to become an egoweak person.
But furthermore the Duke of Gloucester was different in contrast to his family.
"In his family of large, fair, healthy children the dark, undersized, sickly Richard must have seemed like a changeling." 
Even a little child is very sensitive and feels when it is different.
Because of being strange the boy needed more love and approval which is important for developing a superego.
There was nobody, who really cared about him and gave him what he needed.
After his childhood Richardís inappropriate behavior is still supported by his relationship with his mother, the Duchess of York.
In the Drama Richardís mother shows what she thinks of her son in using every chance to express how ashamed she is about Richard being her son. Since his childhood she was grieved instead of being proud and happy about her son , which is shown for instance in the following quotation:
"Therefor, take with thee my most grievous curse,
Which in the day of battle tire thee more
Than all the complete armour that thou wearíst.
[...]Bloody thou art; bloody will be the end." (IV. 4. 188-195)
When he goes out of town they tell him frankly that they both hope that
he will die in a bloody massacre. By this time his mother adds that this
toad" (IV. 4. 145) of a son knows very
well that she has always hated him and that she should have murdered him
even before his birth. The Duchess thinks that one of them will die very
soon. Either he will be killed in battle by the will of the Almighty God
or she will die with deep grief in order to see his face never again (IV.4.
Summing up the relationship between the two was not good at all. If you have a closer look at the way Richardís mother talks to him you will find out that it mirrors aversion against Richard. Hence it underlines and confirms that she does not feel anything for him, which can be a hint at the fact that she never loved him, not even in his childhood. Perhaps her refusal against Richard has even swollen in the course of the time so that Richard now tries to cope with it by exposing himself as a cruel character and ruler.
All these facts affect Richard IIIís egoweak personality and explain his behavior. They make obvious that Richard could do everything to achieve his aim to gain the crown of England because he never really got an idea of the moral standards of the Elizabethan world picture.
If the Duke of Gloucester had identified with someone around him he would have never had left his assigned place.
(1) Richard III Society American Branch, Roxane C. Murph p.1 (www.r3.org)