I believe this is a common problem. At first I was stunned, when a guest of my FI RSVP'd on the website + 3 guests. And the three guests were kids!!!! Don't get me wrong I love kids but I never thought someone would pay for a kid to come to a DW. Then I had people invite family, etc and made a vacation of it. We mad it clear that their family is not invited to the wedding but they are.
When I stopped and took a breath, I calmed down. I told my friends they are welcome to invite their guests. But their guests were not invited to the wedding. We were not responsible for their children but we would make accommodation for them ( but there is no baby sitting service available)
As for guests who I thought were single that chose to bring a friend. I feel for them. (I was single not to long ago) Who wants to go stag to a tropical destination alone? I realize it is a big deal but your guests are spending a lot of money to come to your wedding - we felt that the least we could do is let them bring a guest.
So the fact of the matter is that the guest list has increased. However, the guests are so excited about the coming to share in our special day that I just had to breathe and absorb there excitement and let the rest go. Pick your battles and if the budget rules then limit your guests numbers - people will understand.
This does not mean we have not drawn a line in the sand (so to speak) but if their guest was someone special we did concede.
Good Luck!