The suffix that controls size
X stores avatars on pbs.twimg.com and appends a size suffix to the filename: _normal, _bigger, _200x200, _400x400. Remove the suffix entirely and the CDN serves the file as it was uploaded.
Measured on a real account, that difference is large. The _200x200 version came back at 7 KB. The _400x400 version was 21 KB. With the suffix stripped completely: 25 KB — roughly three and a half times the timeline version. This tool strips the suffix and verifies the result before offering it.
What the original size actually is
There is no single answer, because X does not upscale. The stored file is whatever was uploaded, and X caps avatars at 400×400 on upload. So "original" here means the uncompressed 400-pixel file rather than something dramatically larger. Any tool promising a 1000-pixel X avatar is either upscaling it afterwards or describing a different platform.
Handles change, accounts do not
An X handle can be changed at any time, and the old one becomes available for someone else to claim. If a lookup returns the wrong person or nothing at all, the handle you have may be out of date. Opening the profile and copying the handle from the address bar is the reliable fix.
Protected accounts
Avatars on protected accounts stay publicly visible — the protection covers posts, not the profile picture. If a lookup on a protected account fails, it is usually a stale handle rather than the privacy setting.