I gained a bunch of weight over the last few years and was like 20lbs overweight, now I'm at the high end or a little over for my height, and still have fat around my midsection. I quit drinking for the most part, and my diet is pretty good right now since getting on anti-depressants and not snacking all night.
I'd like to get some muscles, but I hate gyms. I've been doing calisthenics indoors a few times a week. I also have some dumbells, and will jog or hike 2 or 3 times a week.
Should I think about getting more weights or just stick with this routine for now?
You should add squats to that list.
If you want to lose weight, you just need routine exercise and to cut calories. The kind of exercise isn't super important since cutting calories does the actual work there, but if you try to cut calories without exercising you will feel like you're dying, so the exercise is still important.
If you want to gain muscle mass, the level of resistance is a big part of it, and serious programs will try to increase it routinely. This is a problem for body weight routines, since your weight isn't getting heavier, and you'll tend to plateau. That's still fine until you hit the plateau, and it's completely reasonable to continue an all body weight routine until you need to start adding lots of reps to challenge yourself. You should look for more resistance after that point though.
If you're set on those specific exercises anyway, you could try balancing heavy stuff on your back while doing pushups and so forth, I guess. That kind of anime shit is a real hassle though; the reason people like weightlifting is that it's simpler than that.