This is a topic that nobody can just simply answer... "oh..this is what you need to do.. because it works for me." Not-true. Why? Because, everyone is different. Everyone lives in different places (different weather, environments). The physical abilities and agilities of one person are very different than other. Reflexes and reactions are different for different ages of people. Do you live in a summer climate were you wear shorts and a t-shirt everyday.. or in the cold were you wear layers and a jacket everyday. That influences how you can carry to conceal a weapon. But, getting back to the heart of the issue.. the lighter the gun is you carry.. the more you will carry it. A snubbie..small semi-auto.. will be easier to carry all day than a bigger ..heavier gun. Now, if you can support a bigger..heavy gun ...with a bigger ..heavier gun..and thicker holster.. this will help and will make it easier to carry. But, there you go...because it makes it harder to conceal for carrying purposes. What does a carry gun mean to you? How will you be dressed when you are carrying?
Can you carry your Sig.. yes.. but would a G19 be more comfortable..in my opinion and experience yes ..it would be easier to carry than a Sig.. but would a smaller Glock (G26) or a Ruger LCP or a snubbie be easier to carry than the compact G19 Glock.. yes.. the smaller and lighter the better.. but it depends on so many things. Do you own or want to carry something smaller? Do you want/feel comfortable with something smaller...? When I look at a carry gun.. I go for the smallest I can get a way with..that I feel like can do the job for me or for why I'm carrying on that day.. If it's snowing and cold.. I would carry any bigger handgun.. if it's over 100 degrees out side.. the small snubbie or semi-auto.. is a better choice..
Can you carry your Sig.. yes.. should you.. that's up to you and nobody else.. what's good for the goose is not always good for the gander..

Now, that you have my recommendation.. I can tell you what I did. I started off with a full-size Springfield XD for carry. It was good..but it was a tad on the heavy side and a times hard to conceal. Then I swithced to a Glock 27 .. and that was a great day

because it was lighter and easier to carry, more concealable, and just as accurate as the bigger heavier gun. So the G27 was the primary carry gun. Then, along came the S&W 638 snubbie. Even lighter, even more concealable, and yet again..I downsize to a lighter gun.
It carrys lighter than my Glock. As of now the snubbie is the best "carry gun" for hot weather and that's what I use it for. If I wear a jacket or have a way to conceal better.. I go back to the Glock etc. What do I like the best.. without a doubt I love my Glocks and
much prefer a Glock to any other kind of handgun on the market today. Do I always carry one..no I don't. Carrying changes somethings.. If I had to grab a handgun for any given situation.. I'd grab the Glock.. G23.

.. perhaps you should get the G19 too and rotate with the Sig..