This is an excerpt from Shakespeare's As You Like It.
Come, shall we go and kill us venison?
And yet it irks me the poor dappled fools,
Being native burghers of this desert city,
Should in their own confines with forked heads
Have their round haunches gored.
Indeed, my lord,
The melancholy Jaques grieves at that,
And, in that kind, swears you do more usurp
Than doth your brother that hath banish'd you.
Today my Lord of Amiens and myself
Did steal behind him as he lay along
Under an oak whose antique root peeps out
Upon the brook that brawls along this wood:
To the which place a poor sequest'red stag,
That from the hunter's aim had ta'en a hurt,
Did come to languish, and indeed, my lord,
The wretched animal heaved forth such groans
That their discharge did stretch his leathern coat
Almost to bursting, and the big round tears
Coursed one another down his innocent nose
In piteous chase; and thus the hairy fool,
Much marked of the melancholy Jaques,
Stood on the extremest verge of the swift brook,
Augmenting it with tears.
But what said Jaques?
Did he not moralize this spectacle?
O, yes, into a thousand similes.
First, for his weeping into the needless stream;
'Poor deer,' quoth he, 'thou makest a testament
As worldlings do, giving thy sum of more
To that which had too much:' then, being there alone,
Left and abandon'd of his velvet friends,
''Tis right:' quoth he; 'thus misery doth part
The flux of company.' Anon a careless herd,
Full of the pasture, jumps along by him
And never stays to greet him; 'Ay' quoth Jaques,
'Sweep on, you fat and greasy citizens;
'Tis just the fashion: wherefore do you look
Upon that poor and broken bankrupt there?'
Thus most invectively he pierceth through
The body of the country, city, court,
Yea, and of this our life, swearing that we
Are mere usurpers, tyrants and what's worse,
To fright the animals and to kill them up
In their assign'd and native dwelling-place.
Jaques(the person being referred to in the conversation between Duke Senior and the First Lord) is the kind of person that gets "in a very deep mood quite fast, even though the situation is not that serious". People call him melancholic for this reason.
a : depression of spirits, dejection
b : a pensive mood
If the situation is not very serious but the person takes it seriously, you can simply call him pensive.
quietly sad or thoughtful