OK, let me say it this way:
The Straddle bet is technically NOT a Raise, in that when the action gets back to the Straddler (usually the UTG player) that bet is live and the straddler can raise again. I suppose, if you want to get real technical, you can say that the straddle bet increases the minimum bet FOR THAT BETTING ROUND, but ONLY for that betting round. It does not change the minimum bet amounts for any other betting round in that game. For the most part, the straddle bet is intended to stimulate action.
You are playing LIMIT hold'em, 3 - 6 with blinds at 1 and 3. The UTG player, before the deal, straddles for 6. To call the straddle each player must put 6 into the pot. If a player wants to raise, the amount of the raise would be 3 for a total of 9. Lets assume there is no raise preflop (other than the original straddle), although when action gets back to the Straddler, that player can raise. Players that do not fold have to put a total of 6 into the pot. Remember this is all preflop. After the flop, the MINIMUM bet is again 3. After the Turn and River the MINIMUM bet is 6.
Don't confuse the effect of a straddle with that of a KILL. In the case of a KILL, the minimums are effectively doubled. Using the example above (assuming NO Straddle) if the Kill is On, then this becomes a 6 - 12 game with blinds (usually) at 3 and 6.
Now change the game to NO LIMIT hold'em with blinds at 1 and 3. Again the UTG player, before the deal, straddles for 6. To call, each player must put 6 into the pot. If a player wants to raise, the minimum amount of the raise would be 6 for a total of 12. Lets assume every player calls the straddle bet of 6 through the BB. Now the Straddler (the UTG player now has the option of raising) and again the MINIMUM raise would be 6. Again this is all preflop. After the Flop, the Turn and the River, the minimum bet is 3.
From Wikipedia:
"Live straddle
The player immediately to the left of the big blind ("under the gun", UTG) may place a live straddle blind bet. The straddle must be the size of a normal raise over the big blind. A straddle is a live bet; the player placing the straddle effectively becomes the "bigger blind". Action begins with the player to the left of the straddle. If action returns to the straddle without a raise, the straddle has the option to raise. (This is part of what makes a straddle different from a sleeper because a sleeper does not have the option to raise if everyone folds or calls around to him.) The player to the left of a live straddle may re-straddle by placing a blind bet raising the original straddle.[3] Depending on house rules, each re-straddle is often required to be double the previous straddle, so as to limit the number of feasible re-straddles.
Straddling is considered poor long-term strategy by most experts, since the benefit of obtaining last action is more than offset by the cost of making a blind raise. Because straddling has a tendency to enrich the average pot size without a corresponding increase in the blinds (and antes if applicable), players who sit at tables that allow straddling can increase their profits considerably simply by choosing not to straddle themselves."
I hope this helps and doesn't confuse things.