Cannot Achieve Smooth Infinite Movement

I am making a platformer game and after about a week of trying several hours per day, I cannot seem to make the player and camera move smoothly to to right. I thought at first it could just be too many scripts running at the same time in my project, so I made a new dirt-simple project to see if the problem was replicated. The new project consists of the main camera, a sphere as the player, and a few immobile cubes to see the movement better. Nothing else. Here is a screenshot to demonstrate the simplicity:

Without fail, every 2-3 seconds there is a sharp and very noticeable stutter in the movement. Right now, I have the movement set up by updating the velocity of the rigidbodies attached to the player and the camera. However, I have tried every approach I could think of by using Translate(), updating transform.position, using AddForce() on the rigidbodies, etc. and the problem still persists. Also, I have tried using Update(), LateUpdate(), and FixedUpdate() and the problem exists in all of them. Here is my current code (attached to the player), which I cannot imagine could be optimized any more.

using UnityEngine;
using System.Collections;

public class TestMotion : MonoBehaviour
	private Rigidbody2D _playerRB;
	private Rigidbody2D _cameraRB;
	private Vector2 _velocity;

	void Start ()
		_playerRB = gameObject.GetComponent<Rigidbody2D>();
		_cameraRB = Camera.main.GetComponent<Rigidbody2D>();
		_velocity = new Vector2( 200.0f * Time.deltaTime, 0.0f );
	void LateUpdate()
		_playerRB.velocity = _velocity;
		_cameraRB.velocity = _velocity;

I read that this problem occurs for some people in the editor, but not when their game is published, so I tried porting the project to Android and iOS but the problem is there too. It is unfathomable to me that such a seemingly simple problem has been so difficult to solve. I am consistently running at between 68-70 FPS in the game view, so I don’t think the issue is related to the frame rate. Also, my computer has a 4.5 GHz CPU, a GPU with 12GB VRAM, and 32GB RAM, so even if the issue was related to unoptimized code I wouldn’t expect it to be so noticeable. I am desperate for a solution because I really want to publish my game. Any help in figuring out what my problem is would be greatly appreciated.

You shouldnt really move your camera with a rigidbody…

Update your _playerRB.velocity in FixedUpdate().
Then set your Camera.main.transform.position = _playerRB.position.
Use an intermediate variable (Vector3 newPos) so you can set an offset/distance for the camera.

Vector3 newPos = _playerRB.position;
newPos.z -= 10f; //Think it's negative is infront in 2D-view.
Camera.main.transform.position = newPos;

You could also smooth camera movement with Vector3.lerp().
In that case it would look like this:

float Lerprate = 15f;
Vector3 newPos = _playerRB.position;
    newPos.z -= 10f; //Think it's negative is infront in 2D-view.
    Camera.main.transform.position = Vector3.lerp(Camera.main.transform.position, newPos, Time.deltaTime*lerpRate);