Would heavier clothing solve the problem of bone and muscle loss in Martian gravity? It doesn't have to be a perfect solution, I just don't want my Martian colonists to be total wimps compared to Earthlings.

No; probably

Your skeletal muscles are not the most important muscles in your body. That would be your heart. Unless you can add weights your blood, then your heart will get weaker as you spend more time on Mars. The amount of force it takes to pump blood from your heart to your head depends on the hydrostatic force of blood at that vertical distance; so a this required force lowers, your heart gets weaker.

This same argument would apply to any internal muscular structure in your body, and possibly some external ones as well. There are some things you just can't weight.

As a second reason, the reasons for astronaut's bone density loss in space is not well understood. This mass loss is caused by calcium being removed from the bones into the blood, and it starts days after getting into space. Now, we don't really know if an extended stay on Mars at ~30% gravity will have the same effect, but we could probably assume that there will be some sort of effect.

So in conclusion, even if you weighed your clothes perfectly to simulate the musculo-skeletal effect of being on Earth, your internal muscles, in particular your heart, will still be weaker; and your bones may still lose calcium due to some unknown effect of lowered gravity.

Runners on Earth use weights for strength training

In fact, it's exactly what you're asking about. Joggers and runners use weights to increase their strength above what our local gravity can give them. I've personally used weights like these:

Photo Courtesy Amazon.com.

Wrist weights and even torso weights are also used.

So, yes, certainly. Weights can be used to compensate for the loss of muscle due to lower gravity just as we use them to increase muscle in our native gravity.

But it would be uncomfortable to use them all the time. And while weights like this can compensate for muscle loss, they can't compensate for your body's natural adaptation of heart, lung, and other internal organs to the lower gravity. Over time, no matter what you do, you will eventually become unable to return to Earth for long periods of time.¹

_{¹â€ƒYou know, I say this, and lots of people will be willing to believe it... but humanity is remarkably adaptable. I wonder, really, if the 10th generation martians would actually have massive difficulties returning to Earth. I can see the point with full weighlessness, but we really are good at adapting. I'm not willing to rule it out — at least not completely.}

weighted clothing may help some with your skeletal muscles but would not mitigate the effects on your circulatory system there however could be a few ways to change that when dealing with earth standard gravity your martians could wear extremely tight clothing on lower extremities for working periods kind of like a g-suit fighter pilots wear
https://en.wikipedia.org/wiki/G-suit

the other options is to as part of training for the trip complete a work out every day under increased gravity maybe in some type of turbine or centrifugal force machine or maybe have a space station just for the training.
I think using a combination of the two along with the weighted clothing your martians may still experience some fatigue but it should be manageable.

It might help somewhat, but there are a lot of biological functions inside your body that won't like the low gravity. If we ignore those than yes, more weight would make them stronger, unlike more gravity which would hurt their innards and stuff.