I’m gaining weight now that I’m exercising

I tend to eat more when I start exercising so I have to count calories or at least be super aware of what I'm eating.

I think it is muscle gain (I am definitely a mesomoprh and gain muscle easily) but it's water retention as well, something to do with muscle tearing then getting stronger. You do need to drink more water but not too much - watch your pee, if it's colourless you are drinking too much water, if it's pale yellow, you're spot on, dark yellow - too little.

When I was younger I would put weight on slightly for two months when increasing exercise, recently it has been more like six months. I've just started to lose weight but have to eat a lot fewer calories at 46 to lose weight than I did at 26.

Ditch the scales and get a tape measure.

Don't fall into the trap of eating back calories burnt. I used to swim for exercise, now I swim for fun and go to the gym because I eat like a horse after a big swim!

Agree that it's not likely to be muscle, unless you're really going for it. Do you measure yourself in addition to weighing yourself? If not, I'd suggest doing so. Your weight might increase a bit just because of water retention or some other reason but you could find that you're measurements are de-creasing at a steady pace in line with your exercise/calorie intake.
Also, in regards to your food, do you carefully monitor what you consume or do you just keep a mental note? It's incredibly easy to miss calories that you might not have factored in. Using an app like My Fitness Pal to track every calorie you consume (drink too, not just food) will help highlight if there's something you are eating/drinking that you didn't realise was actually totting your daily total up by more than you anticipated.

How much is a few lbs weight gain -- 3? 10?

There are hard physical limits to how much muscle a woman can gain (or lose). You can't turn gain many kg of muscle unless you started bedbound.

Over 7 weeks 1-3 lb extra as muscle might be plausible starting from a low place, with a moderate exercise regime, but not 7-10 lbs.

While it's true that muscle weighs more than fat, I'd be surprised if you were building muscle with the exercises you're doing (not a criticism at all but it's quite hard to build muscle). It's more likely to be water retention but is not unexpected.

Muscle is more dense than fat, so if you're replacing the latter with the former it's to be expected.

If you're burning fat but adding the same volume of muscle, it'll weigh twice as much. The picture below demonstrates how.

I try and avoid scales and go by how I look and feel instead Keep it up!

You’re likely building muscle OP and muscle weighs more than fat. But it could also be that due to getting more exercise done you are eating a little bit more and haven’t noticed?
I have lost over 3 stone and in the past 3 years and it has had its ups and downs. When I started lane swimming 5 times a week I was incredibly frustrated to be putting on a few pounds here and there. Then it dawned on me that my body was still changing in a flattering way, so I was building muscle tone. I also increased my water intake to limit hunger a bit more (swimming makes you so hungry in my opinion).
Good luck, give it time and plenty of it!! You will get there.