You are calling the function at all checkbox and just toggle the state of the button each click at the checkpoints.
I performed some readjustments in your code, follow some of them:
1-I placed a text on the button to make it visible.
2- I added a id button to change its state by script.
Besides, the code is all commented, in case you have any doubts, let me know.
//capturando evento de click e touch(mobile) em todos os checkboxs
$('input[type="checkbox"]').on('click touchstart', function(){
    //capturando a quantidade de checkboxs checados
    let quantCheck = $('input[type="checkbox"]:checked').length;
    
    /*verificando se o número de itens checados é diferente
     de zero para então mostrar o botão*/
    if(quantCheck != 0) {
        $('#botao').css('display', 'block')
    } 
    else {
        $('#botao').css('display', 'none')
    }
});
#botao{
    display: none;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<form>
   <table>
    <thead>
      <tr>
          <th></th>
      <tr>
    </thead>
      <tbody>
       <tr>
        <td><input type="checkbox"></td>
        <td><input type="checkbox"></td>
        <td><input type="checkbox"></td>
       </tr>
      </tbody>
    </table>
    <button type="submit" class="tiny button" id="botao">
    Enviar
    </button>
</form>
 
 
Obs: I added the event touchstart to support the touch event on touch screens.
Event reference
  touchstart: https://developer.mozilla.org/en-US/docs/Web/Guide/Events/Touch_events
If you prefer a method using only vanillaJS:
//capturando todos os checkboxs
checks = document.querySelectorAll('input[type="checkbox"]');
//adicionando evento de click em todos os checkboxs
checks.forEach( function(ck){
    ck.addEventListener("click", function(){
    
        //pegando a quantidade de elementos checados
        let checked = document.querySelectorAll
        ('input[type="checkbox"]:checked').length;
        
        let botao = document.getElementById('botao');
        
        // se a quantidade de elementos checados for igual a 0, então esconde o botão
        if(checked == 0){
            botao.style.display = "none";
        } else {
            botao.style.display = "block";
        } 
    });
});
#botao {
    display: none;
}
<input type="checkbox" />
<input type="checkbox" />
<input type="checkbox" />
<input type="checkbox" /> <br> <br>
<button id="botao"> Botao!</button>
 
 
							
							
						 
I can create a version of your code using
jqueryif you want.– Jorge.M
If it works out, it could be yes.
– KevinF
Possible duplicate of Hide/Show when checkbox is checked or unchecked
– LeAndrade