Frequent punctures, is my weight the problem?

Yes, good advice here, esp re: ”pinch flats“ —sometimes called “snakebites“ because you’ll see two parallel holes. I learned this the hard way, too: check tire pressure is near or @ the maximum psi printed on sidewall before every ride, even *daily! Evidently, *all tubes lose air gradually; under-inflation has caused three flats here in as many days. Shop did not even mention inflation psi and assumed it was weight-related on our tandem (now my *former shop). Important tip to use your limbs as shock absorbers on street bikes.

A lot of good advice so far. Pinch flats are very likely, but also check the rim strip/tape which protects the tube from the spoke nipple ends on the rim itself. ( the location of the punctures should offer a clue as to the cause of the punctures )

Assuming you have the common 700x23c tires, I'd ditch those skinny tires and put some 700x28c tires on there instead. I'd specifically recommend Continental Gatorskin tires, based on 1000s of miles of personal experience, if you can get them. A properly inflated, larger tire, will be more comfortable, and have fewer pinch flats, while still offering acceptable rolling resistance.

As a 310lbs person, you absolutely must inflate your tires to the max rated value. It's printed on the side of your tire. For safety, it is advisable to also check the rating of your rim, as it also needs to withstand the tension of your tire.

If you ride at 80psi, that means that you have a contact area with the road that's 310lbs/80psi = 3.75inch^2. I.e. a patch of 1 inch x 3.75 inch (that's 2.5cm x 9.7cm), or similar. That's a lot, more than your tires are designed to provide, and it means that your tires are squished flat by your weight. There is simply not enough air between your rim and the road to carry you over potholes, roots, and other unevennesses in the road. Instead, the rubber of your tube will be forced to carry you, and it will fail, giving you pairwise punctures where the rim has pressed through to the bottom of the tire.

Bikes are generally built for persons of norm weight (around 70kg). Any person that's significantly more heavy needs to put the max. rated pressure into their tires. Not more because that's the maximum that the tire is built to handle, but lower pressure will increase the likelihood of pinch flats.

Other than Argenti Apparatus' great advice, if you get punctures frequently, one of the following might also be the case:

You may have a small sharp object stuck in your tyre.

Your rim tape may be worn out or misaligned, resulting in spoke holes rubbing through your tubes (happened to me personally, resulted in about 4 flats within a month before I realized it). You say that you replaced the rim, so this is relatively unlikely, but still worth a check.

Your tyre may be too narrow for your rim.

Increased load (i.e rider weight) on a pneumatic tire does not increase the pressure in the tire. The contact patch on the ground just increases in size until the contact patch area x pressure = load (or the rim contacts the ground).

What might be happening is you are getting pinch flats when hitting bumps or holes. This is when the tire and tube are deformed so much by the impact that the tube gets pinched between the tire and the rim often resulting in two symmetrical holes in the tube.

You can try running higher pressure which will stop the tire from deforming as much. 70-80 psi is on the low side for a road bike 28-23mm wide tires.

If you have clearance in your fork or frame run a wider tire. Also if your wheels will support it consider running tubeless tires, which are of course not susceptible to pinch flats.

Trying to avoid bumps and holes in the road, and standing up slightly to absorb impact through bent arms and knees can also help avoid pinch flats.