The largest weight change happens at camp. Same as the rate that the position experience will grow. That why camp is a good place to make the move. That is if your confident that is the move you want to make.
Depending on your postion requirements , the responsibility you will have that position perform most of the time, is how I change positions .
Really I use the system to get the desired weight I want the player to play at as there is a small positional experience penalty when playing out of postion .
Other thinGs to account for is his intelligence as a smart player will learn his new position quicker. So if your looking for a play now guy you might want him to be a bit smarter. A project could be thought of as dumber player as it might take two or more years to perfect the change.
Some other thing to look at is your coaches as they drive your development of red bars . If that coach has a lesser rating it will be slower. HC is is the most influential .....OC and DC is next and position coaches as they develop the ratings highlighted red on their respective cards.
Same goes for what actually gets developed . If you move a qb to a rb his passing ratings will not go up . The max will actually go down. Same goes if you move a te to oline. For example.
Some if your not totally sure about the position of the player and the has value in other ratings sometimes it is better to develop those then make your desired change. Just to get the most out of the player in case you want to switch him back or trade them.
All these are minor effects but they influence my position changes here and there.