Does larger key size mean larger data size in asymmetric encryption? I'm new to cryptography. I know the larger the key size (like 128-bit vs 1024-bit) the harder the ciphertext is to crack, generally. But assuming everything else being equal, does a larger key size increase the data size compared to the original data in asymmetric encryption? I know AES doesn't increase the data size, but what about RSA? 

I've been Googling my question, but I haven't found a straight answer. I just hope the answer is not "it depends", thus I added "assuming everything else being equal".
In addition to kelalaka's answer, keep in mind that the amount of data that can be encrypted with RSA is relatively small (keysize+padding/8), so most schemes use hybrid encryption to use RSA to encrypt a symmetric key and some other critical information and most data is encrypted using the symmetric key.