My answer is
I am frequently prone to distraction,
When bored, you are prone to distraction.
But often I am making the big decision.
A board is a group of people constituted as the decision-making body of an organisation.
Many a tunnel has been me,
To bore is to make a hole in something so many man-made tunnels are bored.
And I have been many a tree.
A board can refer to a long, thin, flat piece of wood.
Sometimes I can be rolling fast,
A skate board rolls fast
Other how a Baratheon passed.
Robert Baratheon was bored by a boar.
As the game goes on I stayed the same,
A board game is a game that involves moving counters around a board.
Bearing whatever weights had came.
The past tense of bear is bore, so you bored the weights.