Probably not, but up to your DM. The Find Steed spell makes it pretty clear that if a spell is targeting the Paladin it can also target the Steed (such as cure wounds). While spells like Cure Wounds work for both due to the spell targeting the Paladin, this wouldn't as Magic Weapon doesn't target the Paladin, it targets the weapon the Paladin is holding.

Such a horrible spell. Concentration, bad scaling, way too limted, and wording that makes it basically worthless after 5th level. Unless you're in a low magic setting (in which case you shouldn't be running into creatures immune to nonmagical weapons until very very late game, in which case this criticism still applies) at least half the party should have a +1 weapon or you should all have common magical weapons. If this spell added a flat plus to any weapon, including ones that already have one; scaled by either increasing the bonus OR the number of weapons affected, was able to affect something like 5-10 pieces of ammunition instead of a single weapon, and didn't require concentration, it might be something people would actually take.

Yes

Could this spell make something like the hemp rope stronger against being broken?  I want to use it to choke out a dragon with my paladin. 

Rakshasa is immune to spells of level 6 or lower but takes double damage from magic weapons wielded by good aligned opponents.  I want to say that they are not able to ignore the double damage from a weapon with this second level spell because the spell is not directed at him.  Is that valid thinking?

I mean, it is always up to the DM, but I would say that you're right. This is a spell cast on a weapon that makes it a magical weapon. So if rakshasa take double damage from a magical weapon, then they'd take double damage from a weapon that this spell has affected. This spell isn't cast on the rakshasa, so it's immunity to spells wouldn't apply.

As other people have said, there are a lot of situations in which this spell is not super useful, but this would be a situation where you'd definitely want this spell prepared.

Why is this spell concentration? I can't think of a single situation in which I'd prefer to use this spell over Shadow Blade.... If I could use it to buff the whole party and not concentrate then sure, but in most all situations (with a few niches) almost every build is going to prefer shadow blade, especially at later levels when everyone has +X weapons anyway....

Question, if you are a pact of the blade warlock, and your conjure an improved pact weapon (gaining that +1), could you then also cast this spell to make your weapon +2. I'm just confused because it says "This weapon counts as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.", but wouldn't that mean in every other sense it is a regular weapon?

The way I understand it, overcoming resistance and immunity to nonmagical weapons is really the only sense in which weapons are ever designated as magical. They can have additional abilities (like a +1), but any time you're trying to determine if a weapon is magical or nonmagical, the answer comes down to whether it overcomes resistance to nonmagical. So... tl;dr, that phrase is just a technical way of saying it's magical but without any extra abilities.

It requires concentration, and you can't cast more than one concentration spell at a time, so your clause is pointless.

Quote from starrybard >>

Honestly to make this ability less lousy I'd home rule that it can apply to magic weapons and also even to a monk's fists

 Why anyone would not use a spear or quarterstaff as a monk at level 1 to 10 is beyond me. They use their dex for monk weapons, lmao.

How to make any weapon a pact weapon:

I'm looking at forge cleric and this spell is the only part I have gripes with. Not only is it just not a great spell, but forge clerics get Elemental Weapon later, which has essentially the same stipulations as this spell but does a d4 of elemental damage while only costing one spell slot higher

WotC changed this in the 2024 PHB to NOT be a concentration spell, which is a much-needed buff for Paladins, Hexblades, Eldritch Knights and Bladesingers (once they get added.)

Would this overcome the resistance to nonmagical weapons? It literally has magic in the title. I would think that yes, it would, but my DM doesn't agree, and I can't find any definite answers.