Запретить изменение размера колонок Qtablewidget

1. void QHeaderView::setSectionResizeMode(QHeaderView::ResizeMode mode)

Устанавливает ограничения на изменение размера заголовка для тех, которые описаны в данном режиме.

2. Попробуйте установит app.setStyle('Fusion')

from PyQt5 import QtCore, QtGui, QtWidgets


class Ui_MainWindow(object):
    def setupUi(self, MainWindow):
        MainWindow.setObjectName("MainWindow")
        MainWindow.resize(483, 180)
        MainWindow.setMinimumSize(QtCore.QSize(483, 0))
        MainWindow.setMaximumSize(QtCore.QSize(483, 22222))
        MainWindow.setStyleSheet("")
        self.centralwidget = QtWidgets.QWidget(MainWindow)
        self.centralwidget.setStyleSheet("QAbstractItemView {\n"
"outline: 0px;\n"
"}")
        self.centralwidget.setObjectName("centralwidget")

        self.tableWidget = QtWidgets.QTableWidget(self.centralwidget)
        self.tableWidget.setGeometry(QtCore.QRect(0, 0, 485, 181))
        self.tableWidget.setStyleSheet("")
        self.tableWidget.setVerticalScrollMode(QtWidgets.QAbstractItemView.ScrollPerPixel)
        self.tableWidget.setHorizontalScrollMode(QtWidgets.QAbstractItemView.ScrollPerPixel)
        self.tableWidget.setShowGrid(True)
        self.tableWidget.setWordWrap(True)
        self.tableWidget.setObjectName("tableWidget")
        self.tableWidget.setColumnCount(3)
        self.tableWidget.setRowCount(7)
        item = QtWidgets.QTableWidgetItem()
        self.tableWidget.setVerticalHeaderItem(0, item)
        item = QtWidgets.QTableWidgetItem()
        self.tableWidget.setVerticalHeaderItem(1, item)
        item = QtWidgets.QTableWidgetItem()
        self.tableWidget.setVerticalHeaderItem(2, item)
        item = QtWidgets.QTableWidgetItem()
        self.tableWidget.setVerticalHeaderItem(3, item)
        item = QtWidgets.QTableWidgetItem()
        self.tableWidget.setVerticalHeaderItem(4, item)
        item = QtWidgets.QTableWidgetItem()
        self.tableWidget.setVerticalHeaderItem(5, item)
        item = QtWidgets.QTableWidgetItem()
        self.tableWidget.setVerticalHeaderItem(6, item)
        item = QtWidgets.QTableWidgetItem()
        self.tableWidget.setHorizontalHeaderItem(0, item)
        item = QtWidgets.QTableWidgetItem()
        self.tableWidget.setHorizontalHeaderItem(1, item)
        item = QtWidgets.QTableWidgetItem()
        self.tableWidget.setHorizontalHeaderItem(2, item)
        self.tableWidget.horizontalHeader().setVisible(True)
        self.tableWidget.horizontalHeader().setCascadingSectionResizes(False)
        self.tableWidget.horizontalHeader().setHighlightSections(False)
        self.tableWidget.horizontalHeader().setSortIndicatorShown(False)
        self.tableWidget.horizontalHeader().setStretchLastSection(True)
        self.tableWidget.verticalHeader().setVisible(True)
        self.tableWidget.verticalHeader().setCascadingSectionResizes(False)
        self.tableWidget.verticalHeader().setHighlightSections(True)
        self.tableWidget.verticalHeader().setSortIndicatorShown(False)
        self.tableWidget.verticalHeader().setStretchLastSection(False)
        self.tableWidget.raise_()
        MainWindow.setCentralWidget(self.centralwidget)

        self.retranslateUi(MainWindow)
        QtCore.QMetaObject.connectSlotsByName(MainWindow)

    def retranslateUi(self, MainWindow):
        _translate = QtCore.QCoreApplication.translate
        MainWindow.setWindowTitle(_translate("MainWindow", "Settings"))
        item = self.tableWidget.verticalHeaderItem(0)
        item.setText(_translate("MainWindow", "1."))
        item = self.tableWidget.verticalHeaderItem(1)
        item.setText(_translate("MainWindow", "3."))
        item = self.tableWidget.verticalHeaderItem(2)
        item.setText(_translate("MainWindow", "2."))
        item = self.tableWidget.verticalHeaderItem(3)
        item.setText(_translate("MainWindow", "4."))
        item = self.tableWidget.verticalHeaderItem(4)
        item.setText(_translate("MainWindow", "5."))
        item = self.tableWidget.verticalHeaderItem(5)
        item.setText(_translate("MainWindow", "6."))
        item = self.tableWidget.verticalHeaderItem(6)
        item.setText(_translate("MainWindow", "7."))
        item = self.tableWidget.horizontalHeaderItem(0)
        item.setText(_translate("MainWindow", "1"))
        item = self.tableWidget.horizontalHeaderItem(1)
        item.setText(_translate("MainWindow", "2"))
        item = self.tableWidget.horizontalHeaderItem(2)
        item.setText(_translate("MainWindow", "3"))

class ExampleApp(QtWidgets.QMainWindow, Ui_MainWindow):
    def __init__(self):
        super().__init__()
        self.setupUi(self)

        self.tableWidget.setItem(0, 0, QtWidgets.QTableWidgetItem('Hello'))
        self.tableWidget.setItem(0, 1, QtWidgets.QTableWidgetItem('World'))

        self.tableWidget.horizontalHeader().setSectionResizeMode(QtWidgets.QHeaderView.Stretch)
        self.tableWidget.horizontalHeader().setSectionResizeMode(0, QtWidgets.QHeaderView.ResizeToContents)
        self.tableWidget.horizontalHeader().setSectionResizeMode(1, QtWidgets.QHeaderView.ResizeToContents)



if __name__=="__main__":
    import sys
    app = QtWidgets.QApplication(sys.argv)
    app.setStyle('Fusion')                                      # <---
    window = ExampleApp()
    window.show()
    sys.exit(app.exec_())