From my experience it seems that it is virtually impossible to beat anyone that is decked out in heavy armor and using a huge sword and shield if your an agile/magic user, for a number of reasons. 
 
1)  Magic seems to miss often in these PvP matches, because you can just role out of the way and there is no way to aim ahead of your opponent.  If there is please tell me.
  
2)  Its virtually impossible to roll behind anyone using big equipment, because they can just as easily move with you by standing still.  Not to mention that someone can easily switch to tower shield without any penalty time wise. 
 
3)  Due to the long range in longer weapons it seems that even though whenever I roll out of the way I can still get hit, even if I'm behind an opponent or very far from them.  This is probably due to lag, but it very irritating when out of no where I get hit when I'm rolling behind them or they somehow magically back-stab me from very, very far away. 
  
4)  Parrying is virtually impossible due to lag 
 
5) Passage ways seem to be mostly narrow and full of potential hazards. 
 
6)  When your the Black Phantom cut-screens will be initiated by you, same with a trap even though it's not meant for you. 
 
7)  Arrows are useless, unless its a straight-away which doesn't matter anyway if they have a shield. 
 
Overall, it may just be that I'm a little upset that my build doesn't work well in PvP, but I reckon that, that has to do with some of the imbalances within the game revolving around PvP.  A big strong warrior just seems to win every time. 
 
If you guys have any tips for me that might help with an agile player please tell me, because I truly can't win unless the guy is surrounded by enemies.  I generally use agile characters. 
 
Also, is there a way to turn off black phantoms.  I definitely enjoy the co-op mode much better when someone isn't trying to kill me.

Also, is there a way to turn off black phantoms.  I definitely enjoy the co-op mode much better when someone isn't trying to kill me.  

Actually heavy armor is laughable in pvp.  Moving slower equals death against a skilled player.  You just need to progress more and get access to new things.  Firestorm is obscenely cheap and works wonders, wrath of god ambushed can be cast on the other sides of walls or obstacles and still hit the enemy, homing soul arrow will go off on it's own after you cast it, acid cloud (which I don't advise using as it is horribly cheap) will take all thier nice gear to 0 durability and break it, etc etc.
 
There is always a counter to anything you will fight in demon's souls, even other players.

you just have to play PvP smart...simple as that.  My newest character seems to be very good for PvP from what I can tell.  The only reason I ever die is because of a laggy player getting hits on my when they aren't even near me.
 
I have light armor so I can jump around as fast as I want.  I had the Dozer Axe in one hand (now I have enough strength for the Brand...even stronger) so that bashes people into the ground and deals a ton of damage.  Also, in that same hand I have a White Bow +5 (white bow upgraded with Colorless Demon Souls).  The bow isn't great unless I'm fighting someone with really weak defense....it's more of a way to annoy a person that keeps running away.  I can just shoot them with arrows nonstop.
 
My left hand I have a Claw.  This is great because my right hand weapon is slow to swing.  So if I'm facing another person with a heavy weapon I can hit them faster with my Claw.  I upgraded it with Mercury so it deals poison damage and also makes them bleed....extremely annoying.  Also in that hand I have a tailsman that I use for God's Wrath.  The good Tailsman that you get during Pure Black Tendency.  My God's Wrath always at the least takes off half of the other guy's health.  Even better, if we are fighting on the Storm level then I can blast them off the ledges with God's Wrath.
 
It seems having heavy armor is incredibly bad for PvP.  Lag is also bad...obviously.  The only person I seemed to of lost legitimately was to a person using a long spear weapon.  They kept a big distance between us and kept poking me...I couldn't do much to fight back.  Just a bit ago, tho, it was 3 on 1 and I took out all 3 guys...that made me feel good :).  When they team up on me and I destroy em all with God's Wrath.

get  over it you big baby