My wife is genetically predisposed to gain weight easily, her weight after my sons birth was less than around 2 pounds more than before the pregnancy. There were a lot of risks so she took it incredibly seriously and the midwives were incredibly impressed when the bang on date baby at 8 pounds 5 was followed by a placenta that was at least this weight. The healthier and fitter the mother the more her body will devote to the placenta to give the baby a the best chance possible, if you have this be very proud of yourself, you deserve it.
The birth was a bad one and there was a risk that I was going to be a single parent. This was due to juvenile abuse she had which had meant her pelvis hadn't developed properly and she shouldn't have been able to give birth to a baby at full term. On reflection she is glad we didn't know and she carried him all the way but I am the person who nearly lost my wife so I have a conflicted view, it was best for my son and that counts for a lot, there's a big but.
The birth involved her losing a lot of blood, not the birth causing this remember it was prior abuse, something the staff weren't totally honest about, but the anaemic look to my wife the following morning was enough for me to see she needed iron and a general vitamin and mineral top up. I checked with the staff ad was allowed to bring food. The NHS doesn't have a lot of budget for food so meat and quality is minimal. It was amusing that other beds with flowers and balloons were occupied by women jealous of the woman with none because new dad was bringing her fresh steak meals etc. to get her strength back. Note for the dads out there, romantic is nice, but the better half will thank you for a good meal.
Activity started the day after my son was born, on reflection if I'd known how bad things were it would have been less but not none. The regime was gruelling, walking down the ward and back 3 or 4 times a day with me as support, total distance must have been almost half a mile, and it was a pace any snail would be ashamed of. she did the pelvic floor etc. consistently and used the walking as an opportunity to straighten herself back up while her abdominal muscles shrunk back to normal size.
A week later out of hospital it got serious. Accompanying me to walk the dogs for toilet trips, gradually progressing to nearly a mile one way with a rest, while I threw things for the dogs to pursue, then getting back. Occasional shopping trips when we knew what we needed and where to get it. Progressing to carrying the baby around the house even when this meant dealing with stairs.
I know this was all pretty pathetic looking stuff especially the last but she was so weakened that she was scared that carrying our son up stairs was literally putting his life at risk, something that tore her apart. Basically there is no-one who should ever tell you that you aren't doing enough and if they do a swift bat to the head should knock some sense into them.
The net result for my wife was she gained more weight in the month following the birth than the 9 months before, and roughly the same in the next few, I was feeding her more than she needed because I was scared and wanted her to live. Sum total was 7 or 8 pounds gain within that year, and she was able to get out with my son in a pushchair to generate a calorie deficit after the first few months and this weight gradually started slipping off, not fast the deficit was minimal.
There are exceptions to this but most babies are born within relationships, if the man prioritises the woman's return to tight belly over her health, I'll leave you to figure out what I think. Take it steady, do what you can but remember your body will have released hormones loosening literally every joint in your body, so load bearing activities are a good way to mess up your recovery and give you a lifetime of pain if done within the first few weeks and after that it will still be a few months before the joints are back to normal. Most people know the abdominal wall stuff and a few other obvious things but there are reasons that post-natal fitness is a speciality and I am not even close to an expert so if you want to do anything more intense than basic walking and swimming check that it is safe for you first.
Baby swim classes are great, my son loved them, I was only able to be there for one due to work, but all the children enjoyed it especially those with mothers walking or swimming with them in the water. Keep it simple and keep to a simple rule 'if in doubt, don't.'