If stretch cords count, <5%.

Think general consensus is time tends to be the biggest limiter in training.
If you have time to work out, it's best put toward s/b/r (in regards to s/b/r performance, not re: general fitness/health).

(as a pure cyclist)

It depends on how you count the time. If you mean the time from when you start the first lift to when you finish the last lift, that'd be <5% (over 2-3 sessions). It's not a lot of time when doing heavy sets. If you include the warmup, stretching, and other non-lifting strength work, 10-15%.

You should get faster. If I increased my training by 20 percent, I would expect to get a lot faster. Weight lifting does not really help you go faster. It might help prevent injury if that is a thing for you, but I've never lifted and I've been running injury-free for 30 years.
This is kind of a hot topic for me because my daughter just quit her college team in large part because she HATED lifting weights and spending a lot of time doing warm-up drills. She came into her freshman season running 8-9 hours a week and apart from one week in five years, she had never been injured. When she ran with me (I was her HS coach), we ran. In the years I coached, we never lifted weights, stretched, or did any warm up drills (other than progressively faster strides) and yet, I never had one injury to my runners during that time. If you are looking to get faster, swapping real training for weights is a good start.

What part of the training cycle?

If it's at the beginning of the cycle it's probably close to 25%. But that's trying to add some muscle and rebuild strength before I had into the 15-10% range for most of the cycle...and it's closer to 20% if I'm being stupid and trying to do triathlon and rugby at the same time.

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Washed up footy player turned Triathlete.

My primary training is strength training and yet it is still a smaller percentage than what it takes for me on the endurance side. On the endurance side I would classify as "serious recreational". Meaning that I train on the bike in structured manner (well not at the moment because I am getting over an illness and excessive overtime at work.) For me, and I am a hard gainer in endurance, I really don't start seeing performance improvements on the bike until I get to about a 10 hour training week.

On impact of performance, I've always been in the camp of sports specific training as the most efficient path. I am guessing that you would improve when putting more focus in your primary training. Just my opinion. Managing the various training stresses weekly are challenging enough if trying to be progressive in each. The more one throws on the pile of various training stresses, the harder it is to manage and potentially harder to be progressive in each.

Just my half cent opinion. :-)

Those two things don't seem to correspond.

10 hour weeks, if done right, can easily get you to a Cat 3 racer. Maybe faster.

A "Cat anything" actual racer is always beyond "serous recreational". The racers on the A+ ride easily drop the rest of the group when the hammer drops.

My guess is going to be intensity. If you actually do train in a structured manner for 10 hours a week, you're not a serious recreational rider. You'd be an amateur racer.

Not all structured plans are equivalent or relevant. Knowing what structured plans you've done would be helpful.

There is no "one size fits all" when it comes to training. Weights will make you faster or slower depending on your age, body composition and training state. Just like anything else. It is making me faster despite training less. But I am a 55 year old male with not too much muscle but not lacking much in the endurance department. I do two complete body sessions per week totalling 1:20 each. Including 10' warm up and 5' cool down.

It maybe a bad idea for a 25 year old with a strong body build and lacking in endurance.

Are you quite sure it's always that simple?

I think this really depends on your definition of recreational. I would say all but a few on ST are recreational athletes. The others are those who are pros or are involved with the sport in some other professional capacity, i.e. coach, equipment seller/manufacturer, etc.

I think it's up to him to decide what he wants to call himself. As far as I'm concerned there's no inconsistency in being an amateur racer, a Cat anything cyclist, training any number of hours a week, and considering oneself a recreational athlete.

My take away from all this is that weight lifting may not make you faster, especially if you sacrifice s/b/r for more lifting. However, as I suspected, a fair amount of people associate weight lifting with injury prevention. I guess this is a result of exercising the muscle groups around those needed for s/b/r. I'm going to reduce from 20% to about 5% and see what happens.