Let's break this up into two separate issues: the slow and the stopping.
First, perform some rational self-evaluation: are you asking people to hike faster than what is expected of the average person? Average hiking speed is only 2mph. Hiking uphill is a lot slower than that. Be realistic. If your slowpoke is in poor physical condition you can't expect much from them. Why are you hiking with people in poor physical condition and expecting them to perform as if they were in shape?
If you're not asking too much, have the slowest person walk point; for some reason they feel a bit more psychological 'pressure' from those behind them and will speed up a bit -- this will also reduce the number of stops.
Engaging in conversation with slowpoke will also create a psychological tether that will help keep the group together.
How do you get a person to eliminate some of their frequent stops? Teach them the 'Rest Step' technique. I'm okay with a person who is 'slow' but continuous, it's the constant stopping that drives me nuts. The Rest Step can really make things better.
Give your human anchor clear objectives, e.g., "We'll stop for water in 15 min...", etc. Sometimes people get the sense that there is no 'end' in sight and they become discouraged. Also, advise them not to keep looking up at the top of the hill they are trying to ascend and emphasize "one foot in front of the other."
On the level of equipment, proper use of trekking poles can really, really improve performance. Again, the key is on proper use of the poles. A lot of folks work against themselves by not using their poles correctly.
What does not work: yelling at them or any other form of aggressive behavior.
Further, if this is a constant problem, you may need to delve into Mr or Mrs Snailspace's motivations for hiking; the frequent stopper may be exhibiting a kind of passive aggressive behavior due to the fact that they want to spend time with you but they don't really care anything about hiking.
However, be patient. A person who wants to be with you and is going hiking as a means for increasing time with you may develop a passion for hiking and backpacking so long as you don't turn it into a grueling slog.
