Can muscles grow without adding weight every week?

Short answer

Yes. Adding reps with the same weight grew muscle with no difference from adding weight. But keeping both weight and reps the same gave only half the growth (11.6% vs 22.9%).

Can muscles grow without adding weight every week?
'Same weight → same stimulus → no growth': is it true?
A common belief is that you have to add plates every week to build muscle. We checked studies on what happens when you add reps instead of weight, and when you add nothing at all.
Can you add reps instead of weight?
Muscle thickness differed by less than 1 mm in most spots
43 people trained their legs for 8 weeks. One group added weight at the same reps; the other kept the same weight and added reps. Differences in thigh and calf muscle thickness were mostly under 1 mm, and the middle front-thigh muscle actually grew 2.8 mm more in the reps group.
What about comparing two legs of the same person?
10% and 11%, no difference
39 people trained for 10 weeks, adding weight with one leg and reps with the other. Thigh muscle cross-section went from 21.34 cm² to 23.53 cm² (10%) on the weight side and from 21.08 cm² to 23.39 cm² (11%) on the reps side, with no difference.
Did adding weight win for strength?
There was almost no difference
In the 43-person study, the heaviest squat people could lift once rose only 2.0 kg more in the weight group. In the 39-person study, the heaviest leg extension went from 52.90 kg to 69.05 kg on the weight side and from 51.67 kg to 66.82 kg on the reps side, with no difference.
So what if you add nothing?
Muscles still grew, but half as much
The arms of 55 people were split into three conditions for 8 weeks. One added weight whenever reps passed 12; another kept the starting weight and reps all the way. Back-of-arm muscle thickness grew 22.9% with adding weight, 11.6% with keeping everything the same, and 1.8% in arms that did not train.
What made the difference was 'a little more'
Either weight or reps went up
The only condition that grew less was the one where neither weight nor reps changed. In the reps group the weight stayed the same, but the reps in each set kept going up. In the 43-person study both groups took every set until they could not do another rep.
Summary: you do not need to add weight every week
But with the same weight and reps, growth was half
Adding reps with the same weight grew muscle with no difference from adding weight. Arms that kept the same weight and reps grew half as much as arms that progressed. Working in an 8-12 rep range and adding weight once you pass 12 reps, starting with reps, is enough.