Your input appears to be a sequence of Python objects; it certainly is not valid a JSON document.

If you have a list of Python dictionaries, then all you have to do is dump each entry into a file separately, followed by a newline:

import json

with open('output.jsonl', 'w') as outfile:
    for entry in JSON_file:
        json.dump(entry, outfile)
        outfile.write('\n')

The default configuration for the json module is to output JSON without newlines embedded.

Assuming your A, B and C names are really strings, that would produce:

{"index": 1, "met": "1043205", "no": "A"}
{"index": 2, "met": "000031043206", "no": "B"}
{"index": 3, "met": "0031043207", "no": "C"}

If you started with a JSON document containing a list of entries, just parse that document first with json.load()/json.loads().

If I understands your question correctly, I think this will solve it:

with jsonlines.open('yourTextFile', mode='a') as writer:
    writer.write(...)

As you mentioned you are overwriting the file, I think this is because you use mode='w' (w = writing) instead of using mode='a' (a = appending)

Use the gzip module's compress function.

import gzip
with open('file.jsonl') as f_in:
    with gzip.open('file.jsonl.gz', 'wb') as f_out:
        f_out.writelines(f_in)

gzip.open() is for opening gzipped files, not jsonl.

Read:

gzip a file in Python

Python support for Gzip