Okay...
Firstly, by consolidating your high intensity stuff, I'm talking about switching this:
Monday: Weights and Cardio
Tuesday: HIIT
Wednesday: Weight and Cardio
Thursday: HIIT
Friday: Weights and Cardio
Saturday: HIIT
To:
Monday: Weights and HIIT
Tuesday: Cardio
Wednesday: Weights
Thursday: Cardio
Friday: Weights and HIIT
Saturday: Cardio
Or something like that. Frankly, I'm of the opinion one doesn't even need to do HIIT while dieting. If you're not lifting crazy heavy weights or dieting terribly strictly, than sure, it can help with partitioning and things like that. But the longer/stricter you diet and/or the more intense your weight training is, the less recovery ability you have. In these instances, doing high intensity cardio simply isn't necessary... the bang for the buck isn't there.
In your particular case, it seems like you're relatively new to all of this. And you're not doing anything crazy in terms of caloric intake. In fact, we'll come back to this in a moment. That said, you should be fine with a handful of sessions of HIIT. I'd stick with two. If you're finding you need to do more than that, something is most likely off with your nutrition.
As for your calories, you say you're 170 lbs and you're eating 2000-2500 calories per day. That's 12-14ish calories per pound of BW which is on the high side for fat loss. If you're finding that this triggers a drop in fat, great. However, you should monitor your progress and if things aren't heading in the desired direction, know that you are on the high side. A more typical range might be something like 10-12 calories per pound for fat loss, but it varies.
Knowing how most people under-estimate their calorie intakes, this is something to keep in mind and adjust according to your progress, or lack thereof.
Also, the foods/nutrients that comprise said calories are also critically important. You indicated that your diet is in check. So hopefully that's the case. I know you also mentioned you're avoiding sugar. Assuming you're getting in adequate amounts of the essentials (protein, healthy fats, veggies, water, etc) I wouldn't sweat sugar terribly much unless you have some sort of intolerance I'm not aware of.
My weight training consists of 2 muscles each day: Biceps, chest on monday; Shoulders, legs wednesday; Back, triceps firday.
Here's a big suggestion.
Read my posts found in this
sticky thread. Then compare and contrast your current training to what's presented there. I think you'll see some obvious differences.
The first thing that stands out to me is that you're training each major muscle group once per week. That's not optimal knowing what we know about muscle adaptation to training. Most of what we care about in terms of muscle growth is recovered within 48-72 hours at the peripheral level which means it would be prime to hit it again.
Something like a full body workout or some sort of upper/lower permutation would most likely be your best ticket.