What is the correct adjective for weight/mass of objects, heavy or large?

I often see in scientific literature the adjective "large" associated to mass/weight, such as "this animal is larger than another"

Are you sure this is what you see? I would be surprised. The default meaning for "large" when it comes to animals and most physical objects refers to overall volume (of the envelope), not to mass/weight. Of course a high volume object is often heavier than a small object but this is not inevitable.

In the following fanciful image, the balloon is larger than the elephant, even though we know that the elephant is heavier/more massive.

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*envelope = a surface that surrounds the shape.

large (adjective)

big in size or amount

Cambridge dictionary

Hence we may speak of a balloon as large (in size) but small (in mass of membrane and gas). Or we may speak of a sandbag that is small in size but large in mass of sand.

A simple statement that something is large merely says that it is large in size. It says nothing about mass. In your example of animals, there is a general correlation between the mass and volume (size) of land animals or fish, so sloppy usage may well say the animal is large, implying that its mass is also large. But this is careless and vague unless the context already clearly relates to mass.

In scientific writing it is bad practice to use the words large or small alone when talking about anything other than size. Such careless use of terms might pass in popular writing on science but should be edited out in anything authoritative. When taking about mass, say large mass or small mass.

Also, in scientific writing it is important to distinguish between mass and weight. A mass of a kilogram weighs a kilogram in earth's gravity but weighs nothing in space.

The mass of an object is defined as the "amount of matter" in an object

Defining mass as "amount of matter" is garbage that is passed for science in middle school. Mass is measure of body's inertia. It is resistance to changing its velocity when a net force is applied.

Mass is measured in kilograms (in SI). Amount of matter is measured in moles (mol).

We can talk about heavy and light bodies as difference in their change of velocity under the same force. Bodies placed on Earth's surface experience the same gravitational pull, so equality of masses means equality of weights. Hence, I don't see any problem talking about "heavy" and "light" in regards to mass. Obviously, "large" does not mean "large mass", it just means large dimensions. Thus, "heavy" == "large mass".