I'm going to split your question into two parts:
- Does a weapon that gives +1 to hit and +1 to damage increase Parry?
I'm afraid your DM is correct, and Parry is not increased. Parry is calculated directly from the character's Fighting Trait, and the only weapon modifiers that can increase it are those that specifically state that they increase Parry.
The reason for this can be explained pretty easily. Just because a weapon can hit something more easily, doesn't necessarily mean it is any better at stopping other people hitting you.
- Can you have weapons that directly give +1 to Parry?
Theoretically, yes you can. Practically though it depends on whether your DM wants to include them in your campaign or not. There are a number of reasons why they may not want to, one of the main ones being that there are already normal weapons that increase Parry, e.g. spears, and introducing magical weapons that do the same would make spears less unique and useful.
For a weapon's bonus to increase Parry, the wording of the bonus must explicitly state that Parry is increased.
See here for an official take on the subject.