If they have Matter Creation, then they could. But if not then they cant create weapons out of nothingness.

Assuming that by "weapons" you mean stuff such as energy swords, whips, axes, etc

They likely could, considering how users of Matter Manipulation have control over atoms, molecules, particles, energy, quarks, etc. They could manipulate those building blocks of matter to seemingly create weapons out of thin air. If the matter manipulator has enough knowledge, skill, precision, and experience; they could likely construct weapons decently fast as well.

However, if by "thin air" you mean creating weapons from literally nothingness, then I don't think they could do that unless they also have Matter Creation, like Yagworm said

A skilled user of matter manipulation would transform any matter into any power granting granting object that would allow him to create matter out of thin air

For a Matter Manipulator to be able to do that it must have Power Infusion, or else it wont work.

And i highly doubt a Matter Manipulator naturally has the ability of Power Infusion, so no, even a skilled Matter Manipulator cant naturally infuse powers to objects. Only when they are given the power to do that.

Oh and btw Power Infusion has no connection to Matter Manipulation whatsoever actually.

Then what does the matter manipulation means

If we'll go like that then every power is useless

The manipulation of physical matter not powers

As again i said, MM needs Matter Creation to create matter out of thin air