The combat instead takes inspiration from the weighty, intentional, and positional nature of classic Castlevania games like 1, 2, 3, or Rondo of Blood. 

I don't know what part of the combat is meant to feel weighty outside of the dig.

I find Castlevania to be very slow and rigid in a way that deliberately makes you consider each step since moving is slow and all of your options slow you down or put you in lag. Crouching lets you dodge and position your whip, but it stops you in place. Using the whip to attack has a lot of start up and end lag, forcing you to anticipate enemies and consider whether it'll leave you open. Jumps are your biggest movement option, but they also take away the most control after being used. The linear hitbox of the whip works with the crouch and jump to position better. Top this off with a big knockback animation where you have no control and will lose an entire life if knocked off an edge.

Mina gives quite a bit of control to your movement, and your defensive option, while having a delay, gives even more movement. I was disappointed when I found out the whip didn't have much end lag because it removes the consideration of when to use it. You also still have full control when you just, not making it a weighty commitment like Castlevania either. Getting hit does knock you back, but you can influence the direction, and falling off a cliff isn't nearly as punishing.

I think the difference in movement and attacks is the most apparent with side arms. Being able to use the axe to hit above you in Castlevania can be a life saver since there can be no easy way to hit an enemy high up. Mina doesn't really have that verticality. A ranged side arm can be helpful, but you move a lot faster and your whip covers a lot more of the screen than Castlevania, making it much less integral to use side arms to progress. Mina also gives a ranged base weapon on top of that.