NormanTheGr8 Loc: Racine, Wisconsin

Or why not rip out the carpet and go with a hardwood floor ?

Dikdik Loc: Winnipeg, Canada

TMurphy has a good solution. The clear plastic floor protectors for offices are pretty rigid, light weight weight and fairly maneuverable. You could also use a 4'x4'x3/8" piece of plywood.

Dik

olemikey Loc: 6 mile creek, Spacecoast Florida

Laminate Flooring panels, the kind that lock together... a couple boxes would allow you make whatever size you need, tape on the backside or underside would help hold them together. There are also garage/gym style lock together pads that would help, or office style clear plastic/acrylic panels that folks use so their office rolling chairs will roll easily while still showing the carpet underneath and these are also available in a few diff. sizes. There are some options. Home Depot, Lowes, Office Depot, Staples, flooring centers, etc.

traderjohn Loc: New York City

Even if it were tongue and grove it has no solid foundation and would separate. I think the person's idea about rigid plastic with those little spikes is the best.

sippyjug104 Loc: Missouri

These are interlocking floor tiles. There are an abundance of styles, colors and textures for locking floor tiles. Some are soft that are used for exercise flooring and some are firm. You can lay down the area that you need and easily pick them up when you are done and store them away.

Dahveed Loc: Minneapolis

Thanks, E.L., anything lighter than plywood is worth a look.

Dahveed Loc: Minneapolis

Thanks, olemikey, these are all good options to investigate.

olemikey Loc: 6 mile creek, Spacecoast Florida

Those are the same type that I have and they would work fairly well on carpet (probably dependent on how thick the underlayment/padding is....but they do work, and are easy to store. I also have a clear plastic one in my little office (over carpet) area and it is even better....it would be a little harder to store (the one I have is approx. 4' by 5 1/2', bought it years ago) they do come in various sizes.

ChristianHJensen

Luan will get destroyed if you walk on it on top of carpet

I would personally use a sheet of 1/2" birch ply. If a full sheet is tough to move around in the room - cut it is half and mount a piano hinge (4 feet long) on the underside of the cut - that way you can just pick it up and fold it in half

Photocraig

3 options:
Use plywood that is 1/4 inch thick. It has more flex than 1/2 inch, but is 1/2 the weight.
Use Hardboard or Masonite which is even thinner and lighter. The key is that there are no joints and seams that will flex independently and show as hard lines or corners in the photograph--or worse, expensive tears.
Inexpensive rugs, that don't look like bedroom carpet in different colors may provide a base layer and contrast to the seamless background, and still be durable.

The issue is what you're trying to accomplish and what you're trying to avoid that the carpet causes. But since the flooring solution needs to bear the model's weight plus any furniture/props in the scene, a solid base is required.

Avoid shoes, especially high heels as much as possible with seamless. The stuff is expensive and fragile.

All floor work and moving of heavy seamless rolls etc. should be done BEFORE lighting stands and lights and modifiers are within range--and the model arrives into the studio shooting aea. Think about getting help before the shoot starts since for a small person, large sheets of even masonite can be unwieldy.

Caution, unfinished edges of plywood are splinter factories. Either sand and finish or tape the edges and use work gloves when handling.

YouTube has several videos on a "Spare bedroom studio." One by Julia Ratti is quite good and she's a noted pro.

chasgroh Loc: Buena Park, CA

...most here are recommending ply, as I do. Right now I'm sitting on 3/4" ply *screwed* through the carpet below and into the wood sub-flooring. I roll around on it, it's where I have my computers, scanners, printer and other informational aspects of my different passions. Now, the OP's resistance seems to be about the weight and bulkiness? Get some help. Move what gear you have to, and make your flooring project semi-permanent. You will be much happier than dealing with flexible alternatives...that's why 3/4"...it won't flex. Even 1/2" would be marginal, but if screwed down probably would work (the luan idea would be much too flexi for me, remember, you're going on top of carpet). I build things (yes, I'm a tradesman...40 year apprentice carpenter/cabinetmaker) and immediately gravitate to strength, so YMMV. Oh, if you're on a slab, even more of a case for thicker ply, because there is no easy attachment...

Stardust Loc: Central Illinois

You are correct if the lauan was used for permanent, high-traffic use over carpet but for light use with the OP requested. First, apparently will be sparingly used by his "if wanted to extend roll paper for a full-length photo" and want a "cheap & easy way". 1/4" lauan goes for $6-7 a sheet where I live, 1/2" birch about $35-40 a sheet, plus lauan probably 1/3rd the weight. (One person actually suggested trying to toss around 3/4"-4x8 sheets of plywood at around 75-80 lbs per sheet)

E.L.. Shapiro Loc: Ottawa, Ontario Canada

You are very welcome.

At the studio we used TEMPERED MASONITE- it is extremely tough. In one room we have 3 4x8 sheets to cover the floor with enough space for the wide rolls of seamless paper or some of the longer canvas background we have to accommodate the floor in full length images. In a smaller space we cut some of the 4x8 sheet in half, lengthwise, and hinged them together so the fold up out of and out of the way the way for easier storage.The rough edge tends to grip the carpet nicely so it wont slide around. The smoot side is a good base for the paper.

We use the 1/8 in regular non-tempered Masonite in frames made of 1x2 pine to make flats and "V" reflector panels. They can be painted white or lined with aluminium foil or Rosco reflective materials. Again, I cut them in half and hinge them together so the are free-standing and easily stored and transported. Masonite is less expensive that plywood and significantly lighter in weight that pressed boards such as Aspeinte etc. I get them cut at the lumber yard because the dust is messy. Once they are constructed they last for many years in hard service.

Grey Ghost

Simply remove the carpet and put down an inexpensive solid surface floor covering.

E.L.. Shapiro Loc: Ottawa, Ontario Canada

It's a "home" studio- I assume the OP does not want to remove the carpet from a room that he uses for a temporary setup. He just wants to find a material to prevent the seamless paper from being perforated or excessively damaged when folks walk on it so he needs a material to support the paper.