Having a second child is very much an individual decision, and it seems like you have thought about some of the things related to it. Here's my take on some of the possible concerns. My opinion comes from someone in a middle class US household with two parents and two elementary-age children.
Having a second child is, unsurprisingly, nearly twice as expensive as having a single child. Numbers below are from The Cost of Raising a Child, put out by the US Department of Agriculture based on the Consumer Expenditures Survey, which is sponsored by the US Buruea of Labor and Statistics. Numbers will obviously vary significantly by location, parental circumstances, etc., and are meant to be illustrative of one reasonable value.
Each child in a two-parent two-child household costs an average of $233,610 from 0-17, plus the cost of college, or nearly $13,000 per year. In a single child household, that number is 27% higher (or around $16,500). So the second child will cost you almost $10,000 per year in addition to the cost of the child you already have.
Are you prepared to pay that additional $10,000? Are you in particular prepared for the years where it's actually higher (the later years, if you're curious - around $900 per child on average for 15-17)?
When we decided to have a second child, we did so in the realization that the children would dominate our finances for years to come. We both have good jobs with solid incomes and skill sets that are always in demand, so we were able to make that choice comfortably - but it was a major factor.
Having a second child means you have more demands on your time. The sum of (time for yourself) + (time for your partner) + (time for each kid) is still 24 hours minus sleep, after all.
With a second child, you have less time for yourself/your partner AND less time for your children individually. Are you the sort of person who is energized and rewarded by spending time with your children? Do you currently spend a lot of time doing things other than child-rearing, and do you anticipate it being a problem that you reduce that time?
Assuming you sleep around 8 hours a day, you have 16*7 = 112 hours in the week available. How do you plan to split those hours up? That's about 70 hours after factoring in work, of course.
The Bureau of Labor Statistics estimates that Americans spend over 2 hours per day where their primary activity is childcare when the youngest is under 6, dropping to 1 hours for children 6-12. They don't break it down (on that page, anyway) for number of children in the household, but you can be confident it's higher for 2 child households than one. They spend another 5 hours per day in secondary childcare, meaning they're doing something else while being responsible for children.
That means 7 hours a day involve a child - plus 8 hours of sleep, plus work. Given the average number of children is 2, this estimate is probably representative of a 2 child household; your 1 child household will either have more time to devote to the 1 child, or will have more time for the parents to do other things.
In my case, I am someone who greatly enjoys childcare-related activities. As such, it wasn't a big concern to me that I lost some of my personal time. It's not ideal for my wife I think, more so than myself, as she'd rather have more "us" time than we have now, though, and isn't as "recharged" from caring for children as I am. Not to say she wishes we had only one child - very much not the case - but it was definitely a "cost" to her (and thus, to us). Make sure you and your partner both are on the same page there.
Attention available per child
This is really an offshoot of Parental Time, but: with one child, you have far more attention to devote to that one child, whereas for two children you can't. Noting the numbers above - 2 hours spent in primary childcare, 5 hours spent in secondary childcare, per day - that 2 hours is where you're really focused on your child(ren), and doesn't have a ton of room to move up for more children. With two children, you'll divide a perhaps somewhat larger number (again, that 2 hours is probably for 2 children) in half, while for one child you'll have a perhaps somewhat smaller number all to one child.
Having a second child means activities (gymnastics, music, dance, soccer, etc.) will be either done together, or less hours in activities per child, until they're old enough to go on their own. If they're close enough in age, you can read to them both at the same time - but if not, you'll have to divide the reading between two parents (and even my two children, 19 months apart, go through phases where they prefer separate readers) - which again means less time available per parent for other things (while Mom reads, Dad can be doing the dishes, or the reverse).
That second child does mean that the children can entertain each other to some extent, getting valuable socialization time while at home with Mom and/or Dad doing other things (those 5 hours a day in secondary childcare), on the other hand, as long as they're close enough in age that they can do that effectively.
In our case, we've managed to coordinate activities for the most part; but it's probably meant the younger child has been led to participate in the older child's activities more than they would've otherwise. It's only now that the younger child (6) has really developed a strong preference for other activities, which is making it even more complicated for us - not something I mind necessarily, but it does mean we have said no to some activities for both children that are more time-sucks (soccer, in particular, which around here means 2 practices in the week and a game day on the weekend, even at 8 years old) that we'd otherwise have allowed with a single child household. It's certainly possible - we have 3 extracurricular activities each basically right now per week - but it's definitely a stretch.
You specifically mention "having each other after you're gone". I don't find that very relevant myself, but likely because my family is not very close - they're all in different states, and we see each other rarely; if my parents were gone, the presence of my siblings wouldn't really change things one way or another. But it's definitely something some people do care about; I won't discuss it, though, as I don't know anything about it.
Other than time and money, there's also the concern of space - will you have enough room in your house comfortably for a second child? Not just bedroom space, but you'll need more space for playing. How do you feel about cleaning up, organizing, etc.? That's probably our weakest area - and having two children makes it much harder.
All in all - I think it's a very individual question, but hopefully you get plenty of input as to the potential inputs on the matter. It's definitely not a "by the numbers" decision, despite my numbers in this post - I think it's important to know what the numbers are, but they're certainly not the reason to make the decision by itself.