What are blademancers?
Blademancers are mages (going by the definition "Anyone who uses magic", and not "old man who wears a pointy hat and carries a staff") who can control blades from a distance.
Note: Henceforth I will be using 'sword' and 'hilt' and other such terms, because I am using sword as a default weapon here. Thus when I talk about a 'sword', I mean whatever weapon the blademancer is using.
A blademancer is able to control only those swords that have a specific magical seal/mechanism built into their hilt. Once they have such a sword, they can take control of it. For this, they first reach out and 'feel' (psychically) the blade, then 'take hold' of it. After that they can move the sword as if a disembodied hand was grasping and moving it.
Number: A blademancer can, depending on their level of mastery, control 2-8 blades at a time. Only the weakest of the weak blademancer struggles to move past one, and the average blademancer (not that 'average' and 'weak' is comparable to blademancers. You have to be extremely skilled to even become one) can, in his/her lifetime, attain 6-7 and sometimes 8. Gifted humans, demigods, gods and other such powerful entities can attain even more, but are so extremely improbable as to not factor into worldbuilding at all. They can take control of them at once, and do not need to repeat the 'taking control' procedure for each sword. if a sword breaks, they can take control of a previously uncontrolled sword without letting go of other swords, but that will take time and concentration and may be very hard to do when in an active fight. Number affects mental stamina.
Weight: Each sword in the above given limit is around 1 - 1.2 Kg (2.2 - 2.6 lb). The heavier the sword, the more the effort needed to control it. Weight affects both physical and mental stamina.
Distance: Most blademancers can control swords to a maximum of 3-5 metres away. This is distance from the blademancer to the magical seal, so the weapon can have parts of it outside the limit. Distance does not affect stamina perceivably. Holding a sword 5 metres away is not significantly more difficult than holding it a metre away, though for a very long duration, it can start to affect physical stamina.
Point to note: The weight affects the limit pretty linearly - An 8-mancer holding 4 2Kg swords will feel the same strain, and if he/she holds 8 such swords he/she will get tired twice as fast.
However, the number limit is absolute. A 7-mancer is unable to fight properly with 8 swords not because he/she gets tired more quickly, either physically or mentally, but because of an inability to focus. Using 8 swords will not make one sword weaker, it will mean being bad with all swords being used, or only using some swords at a time while not moving the rest. This is the same as a beginner piano player who can't play with both hands at the same time and upon trying makes a cacophonic mess with both hands.
Thus, using 500 gram swords will not make an 8-mancer be able to use 16 swords. However, an 8-mancer will be able to hold them at the same level of physical strain, and can do things like chucking a few at the enemy while finely using the rest.
Additional limits: Humans are bad at multitasking. It is extremely mentally straining for a blademancer to fight multiple targets not close to each other at the same time with a high level of skill. They are also pretty bad at fighting what they can't see so no fighting behind their back. They can move swords behind them, and doing something like having a sword circle you is easy even when it goes behind their back, but they can't fight someone behind them any better than just slashing in the general vicinity and other reflex actions.
What weapon does it make the most sense to fight with, for a blademancer? Only weapons with one/limited components are allowed, as each component and moving part requires a seal on it. A bow will require a seal on the bow, and the arrow, and so on.
Edits/ Additional Information
Will be updated as requested
E1: Due to the fact that every weapon needs to have a magical mechanism built into it, the weapons do have a minimum weight. Assume 400-500 grams. Magical mechanisms are tedious and expensive to produce, and sometimes some cults or organisations (not necessarily blademancers, but applies to them too) keep it secret how to make them. So a group of blademancers using cutting edge (hehe) magical seals would make damn sure not to leave any of their weapons just lying around, though this is less of a consideration than the time and effort needed ot produce the blade.
E2: The magical seal/mechanism is an actual physical thing, like a carving or a rune, made of its own material. It is not some metaphysical thing or enchantment upon the blade that is there but not in the physical world. It is very much in the physical world.