Is there a reason why a person would tend to play stronger players as
Black and weaker players as White?
Or is it just a coincidence?
To understand this you only have to look at the way the first round of a Swiss tournament is drawn. Following rounds follow similar principles within score groups (groups of players with the same score) and allowing for colour preference (aiming for WBWBWB etc and avoiding BBB and WWW except possibly in the last round).
Suppose you have 16 players who we'll call for simplicity's sake "1", "2", ... "15", "16" where "1" is the strongest, "2" next strongest and so on. Colour for the first round is determined randomly, that is half the time player "1" gets black and half gets white.
The first round draw should look like this when "1" is assigned white:
"1" v "9"
"10" v "2"
"3" v "11"
"12" v "4"
"5" v "13"
"14" v "6"
"7" v "15"
"16" v "8"
As you can see half the time the weaker player is white and half the time black.
When you see deviations in this pattern it tells you one of two things:
1) There was a forbidden pairing which changed the order
2) One or more players who entered the tournament pulled out or missed the first round without telling the arbiter and some pairings were redone to try and ensure that every player had a game.
Note that 2) requires either the agreement of the players involved in the redraw or that the tournament conditions specify that this will happen automatically. The chess world's leading barrack room lawyer, now a FIDE vice president, famously pulled out of a tournament when this happened to him in the first round without his permission and without being part of the tournament conditions.
Occasionally you will see a (high level) tournament where the tournament appears to have been split in two with the top half paired according to the above algorithm and the bottom also paired accordingly. In this case something called "acceleration" has been applied to keep the strongest and weakest players apart for the first round or two. This is done in norm tournaments where the chances of norm seekers in the top half of the field would be ruined if they had to play 2 or more very weak (relatively) players in the early rounds.