When I started this game, I immediately went online (no tutorial) and did some farming tasks (cultivating and planting) with the smaller tractor. Now I decided to go to the tutorial to get a better understanding of the tasks and the tutorial makes me carry a weight in the front of the tractor to balance out the load. Is there any downside to not having a weight in the front of the tractor? I ask as I was able to farm online without the front weight without any issues.
Yes, but not all the time.
It will never be a factor until you put a heavy attachment on, but improper weight distribution can literally lift your tires off the ground. Certain vehicles are heavy enough that this is not a problem, but the smaller tractors, with the larger attachments, will tip backwards or forwards.
I believe I personally ran into this when, in FS15, i put an upgraded fertilizer attachment on the back of the basic, free tractor they give you when you start.
I found some forum posts that talk about it happening a bit, and there are some mods (linked to in the post) that help with weight issues. However, I found a screenshot of it happening, to a somewhat extreme degree: